Multi-User Multiple-Input And Multiple-Output For Digital Subscriber Line

ABSTRACT

A method implemented in a wireless network element (NE), comprising obtaining, via a processor of the wireless NE, a plurality of encoded signals associated with a plurality of downstream (DS) channels in a wireless communication network, wherein the plurality of DS channels form a plurality of DS multiple-input and multiple-output (MIMO) groups, performing, via the processor, MIMO pre-coding on the plurality of encoded signals according to the plurality of DS MIMO groups to produce MIMO pre-coder output signals of the plurality of DS MIMO groups, performing, via the processor, a crosstalk pre-coding across the MIMO groups using a crosstalk pre-coding matrix on the MIMO pre-coder output signals of the plurality of DS MIMO groups to produce a plurality of output signals, with the crosstalk pre-coding matrix computed according to a first DS channel matrix and a DS MIMO channel matrix, wherein the first DS channel matrix comprises first diagonal entries representing first direct channel estimates of the plurality of DS channels at a first subcarrier and first off-diagonal entries representing co-channel interference estimates of the plurality of DS channels at the first subcarrier, a first diagonal block of the first DS channel matrix representing MIMO channels in a first DS MIMO group of the plurality of DS MIMO groups, and wherein the DS MIMO channel matrix comprises a second diagonal block and off-diagonal blocks, the second diagonal block corresponding to the first diagonal block of the first DS channel matrix, and with the off-diagonal blocks comprising values of zeros, and synchronously transmitting, via one or more transmitters of the wireless NE, the plurality of output signals to a plurality of remote wireless NEs via the plurality of DS channels.

CROSS-REFERENCE TO RELATED APPLICATIONS

The present application claims priority to U.S. patent application Ser.No. 15/148,698 filed May 6, 2016 by Amir H. Fazlollahi, et. al.,entitled “Multi-User Multiple-Input And Multiple-Output For DigitalSubscriber Line,” now U.S. Pat. No. 9,948,371, which claims priority toU.S. Provisional Patent Application 62/159,560 filed May 11, 2015 byAmir H. Fazlollahi, and entitled “Multi-User Multiple-Input AndMultiple-Output For Digital Subscriber Line,” and U.S. ProvisionalPatent Application 62/180,457 filed Jun. 16, 2015 by Amir H. Fazlollahiand Xiang Wang, and entitled “Multi-User Multiple-Input AndMultiple-Output For Digital Subscriber Line,” all of which areincorporated by reference.

REFERENCE TO A MICROFICHE APPENDIX

Not applicable.

BACKGROUND

Twisted-pair copper wires were initially designed to carry low-bandwidthvoice telephone signals. Today, twisted-pair copper wires are widelyused to carry high-bandwidth data signals from a central office (CO), aremote terminal (RT), or a distribution point (DP) to customer premisesequipments (CPE) in digital subscriber line (DSL) systems. Asymmetricdigital subscriber line (ADSL)/ADSL2/ADSL2+ described in “Asymmetricdigital subscriber line (ADSL) transceivers,” InternationalTelecommunications Union—Telecommunication Standardization Sector(ITU-T) document G.992.1, 1999, “Asymmetric digital subscriber linetransceivers 2 (ADSL2),” ITU-T document G.992.3, 2002, and “Asymmetricdigital subscriber line (ADSL) transceivers—Extended bandwidth ADSL2(ADSL2+),” ITU-T document G.992.5, 2003, which are incorporated byreference, use a bandwidth of up to a few megahertz (MHz). Very-highspeed digital subscriber line (VDSL)/VDSL2 described in “Very-high speedDigital Subscriber Line Transceivers 2 (VDSL2 draft),” ITU-T documentG.993.2, July 2005, which is incorporated by reference, use a bandwidthof a few tens of MHz. Fast access to subscriber terminals (G.fast)described in the ITU standard “Fast Access to Subscriber Terminal,”ITU-T document G.9701, December 2014, which is incorporated byreference, uses a bandwidth of about 100 MHz or higher.

SUMMARY

DSL communications experience various forms of interference, includingfar-end crosstalk (FEXT). In a vectored system, transceivers at a COside are collocated, but transceivers at customer premises aredistributed. Thus, coordination may only be performed at the CO side tocancel or reduce FEXT. However, in a system where transceivers at thecustomer premise are also collocated, multiple-input and multiple-output(MIMO) processing may be used to utilize FEXT rather than cancellingFEXT to improve performance. In addition, multi-user-MIMO (MU-MIMO)processing may be used to pre-code or cancel FEXT across MIMO groups.However, the computational complexity for MU-MIMO processing is high dueto decomposition of large-size matrices and therefore may not besuitable for implementation in DSL systems. To resolve these and otherproblems, and as will be more fully explained below, matrixdiagonalization is performed on each MIMO group channel sub-matrixseparately instead of a large-size full channel matrix, and MIMOpre-coding and cancellation matrix are computed based on the matrixdiagonalization.

In one embodiment, the disclosure includes a method implemented in anetwork element (NE), comprising obtaining, via a processor of the NE, aplurality of encoded signals associated with a plurality of downstream(DS) channels in a network, wherein the plurality of DS channels form aplurality of DS MIMO groups, performing, via the processor, MIMOpre-coding on the plurality of encoded signals according to theplurality of DS MIMO groups, performing, via the processor, crosstalkpre-coding on the plurality of encoded signals jointly after performingthe MIMO pre-coding to produce a plurality of output signals, andsubstantially synchronously transmitting, via transmitters of the NE,the plurality of output signals to a plurality of remote NEs via theplurality of DS channels. In some embodiments, the disclosure alsoincludes a first subset of the plurality of DS channels forms a first DSMIMO group of the plurality of DS MIMO groups, wherein the methodfurther comprises receiving, via receivers of the NE, a MIMO pre-codingmatrix for the first DS MIMO group at a first subcarrier, wherein theMIMO pre-coding matrix is decomposed from a DS MIMO channel matrixcomprising direct channel estimates of the first subset of the pluralityof DS channels at the first subcarrier and FEXT channel estimates of thefirst subset of the plurality of DS channels at the first subcarrier,and wherein performing the MIMO pre-coding comprises multiplying asecond subset of the plurality of encoded signals associated with thefirst DS MIMO group by the MIMO pre-coding matrix, and/or furthercomprising obtaining, via the processor, a first DS channel matrix,denoted as H, comprising first diagonal entries representing firstdirect channel estimates of the plurality of DS channels at a firstsubcarrier and first off-diagonal entries representing first FEXTchannel estimates of the plurality of DS channels at the firstsubcarrier, wherein a first diagonal block of the first DS channelmatrix represent MIMO channels in a first DS MIMO group of the pluralityof DS MIMO groups, generating, via the processor, a DS MIMO channelmatrix, denoted as H_(M), comprising a second diagonal block andoff-diagonal blocks, wherein the second diagonal block corresponds tothe first diagonal block of the first DS channel matrix, and wherein theoff-diagonal blocks comprises values of zeros, and computing, via theprocessor, a FEXT pre-coding matrix, denoted as P, according to aproduct of an inverse of the first DS channel matrix Hand the DS MIMOchannel matrix H_(M), wherein the product is expressed as P=H⁻¹×H_(M),wherein performing the crosstalk pre-coding comprises multiplying theplurality of encoded signals by the FEXT pre-coding matrix afterperforming the MIMO pre-coding, and/or further comprising obtaining, viathe processor, second direct channel estimates of the plurality of DSchannels at a first subcarrier, second FEXT channel estimates withineach of the plurality of DS MIMO groups at the first subcarrier, andthird FEXT channel estimates across the plurality of DS MIMO groups atthe first subcarrier after performing the MIMO pre-coding and prior toperforming the crosstalk pre-coding, wherein the second direct channelestimates and the second FEXT channel estimates are MIMO pre-coded andMIMO post-coded channel estimates, generating, via the processor, asecond DS channel matrix comprising second diagonal entries representingthe second direct channel estimates, second diagonal blocks eachcomprising second off-diagonal entries representing corresponding secondFEXT channel estimates for each of the plurality of DS MIMO groups, andsecond off-diagonal blocks representing the third FEXT channelestimates, and inverting, via the processor, the second DS channelmatrix to produce a FEXT pre-coding matrix, wherein performing thecrosstalk pre-coding comprises multiplying the plurality of encodedsignals by the FEXT pre-coding matrix after performing the MIMOpre-coding, and/or further comprising assigning, via the processor,values of zeros to the second off-diagonal entries of the seconddiagonal blocks before inverting the second DS channel matrix, and/orfurther comprising substantially synchronously receiving, via receiversof the NE, a plurality of modulated signals from the plurality of remoteNEs via a plurality of upstream (US) channels at a second subcarrier,wherein the plurality of US channels form a plurality of US MIMO groups,performing, via the processor, discrete Fourier transform (DFT) on theplurality of modulated signals to produce a plurality of demodulatedsignals, performing, via the processor, frequency domain equalization onthe plurality of demodulated signals to produce a plurality of equalizeddemodulated signals, performing, via the processor, crosstalkcancellation jointly on the plurality of equalized demodulated signals,and performing, via the processor, MIMO post-coding on the plurality ofequalized demodulated signals according to the plurality of US MIMOgroups after performing the crosstalk cancellation, and/or a firstsubset of the plurality of US channels forms an i^(th) US MIMO group ofthe plurality of US MIMO groups, wherein i is a positive integer,wherein the method further comprises obtaining, via the processor, a USMIMO channel sub-matrix, denoted as H_(i,i), comprising diagonal entriesrepresenting first direct channel estimates of the first subset of theplurality of US channels at the second subcarrier and off-diagonalentries representing first far-end crosstalk (FEXT) channel estimates ofthe first subset of the plurality of US channel at the secondsubcarrier, decomposing, via the processor, the US MIMO channelsub-matrix H_(i,i) into a first matrix, denoted as A_(i,i), a secondmatrix, denoted as W_(i,i), and a third matrix, denoted as B_(i,i),where H_(i,i)=A_(i,i)×W_(i,i)×B_(i,i) ⁻¹, and sending, via thetransmitters, the third matrix B_(i,i), to corresponding remote NEs tofacilitate MIMO pre-coding in a US direction, and wherein performing theMIMO post-coding comprises multiplying a second subset of the pluralityof equalized demodulated signals associated with the first subset of theplurality of US channels by a first inverse of the first matrix A_(i,i)⁻¹, and multiplying the second subset of the plurality of equalizeddemodulated signals by a second inverse of the second matrix W_(i,i) ⁻¹after multiplying the second subset of the plurality of equalizeddemodulated signals by the first inverse of the first matrix A_(i,i) ⁻¹,and/or decomposing the US MIMO channel sub-matrix H_(i,i) by applyingsingular-value decomposition (SVD) to the US MIMO channel sub-matrixH_(i,i) and/or decomposing the US MIMO channel sub-matrix H_(i,i) byapplying geometric mean decomposition (GMD) to the US MIMO channelsub-matrix H_(i,i), and/or further comprising obtaining, via theprocessor, a first US channel matrix, denoted as H, comprising firstdiagonal entries representing first direct channel estimates of theplurality of US channels at the second subcarrier and first off-diagonalentries representing first FEXT channel estimates of the plurality of USchannels at the second subcarrier, wherein a first diagonal block of thefirst US channel matrix H represents MIMO channels in a first US MIMOgroup of the plurality of US MIMO groups, generating, via the processor,a US MIMO channel matrix, denoted as H_(M), comprising a second diagonalblock corresponding to the first diagonal block of the first US channelmatrix and off-diagonal blocks comprising values of zeros, andcomputing, via the processor, a FEXT cancellation matrix, denoted as C,according to a product of the US MIMO channel matrix H_(M) and aninverse of the first US channel matrix H, wherein the product isexpressed as C=H_(M)×H_(ji) , wherein performing the crosstalkcancellation comprises multiplying the plurality of equalizeddemodulated signals by the FEXT cancellation matrix, and/or furthercomprising obtaining, via the processor, second direct channel estimatesof the plurality of US channels at the second subcarrier, second FEXTchannel estimates within each of the plurality of US MIMO groups at thesecond subcarrier, and third FEXT channel estimates across the pluralityof US MIMO groups after performing the MIMO pre-coding and prior toperforming the crosstalk pre-coding, wherein the second direct channelestimates and the second FEXT channel estimates are MIMO pre-coded andMIMO post-coded channel estimates, generating, via the processor, asecond US channel matrix comprising second diagonal entries representingthe second direct channel estimates, second diagonal blocks eachcomprising second off-diagonal entries representing corresponding secondFEXT channel estimates in each of the plurality of US channels, andsecond off-diagonal blocks representing the third FEXT channelestimates, and inverting, via the processor, the second US channelmatrix to produce a FEXT cancellation matrix, wherein performing thecrosstalk cancellation comprises multiplying the plurality of equalizeddemodulated signals by the FEXT cancellation matrix.

In another embodiment, the disclosure includes a communication systemoffice-side apparatus, comprising a processor configured to obtain aplurality of encoded signals associated with a plurality of DS channelsin a network, wherein the plurality of DS channels form a plurality ofDS MIMO groups, perform MIMO pre-coding on the plurality of encodedsignals according to the plurality of DS MIMO groups, and performcrosstalk pre-coding on the plurality of encoded signals jointly afterperforming the MIMO pre-coding to produce a plurality of output signals,and a plurality of transmitters coupled to the processor and configuredto substantially synchronously transmit the plurality of output signalsto a plurality of remote NEs via the plurality of DS channels. In someembodiments, a first subset of the plurality of DS channels that forms afirst DS MIMO group of the plurality of DS MIMO groups, wherein thecommunication system office-side apparatus that further comprisesreceivers coupled to the processor and configured to receive a MIMOpre-coding matrix for the first DS MIMO group at a first subcarrier,wherein the MIMO pre-coding matrix is decomposed from a DS MIMO channelmatrix comprising direct channel estimates of the first subset of theplurality of DS channels at the first subcarrier and FEXT channelestimates of the first subset of the plurality of DS channels at thefirst subcarrier, and wherein the processor is further configured toperform the MIMO pre-coding by multiplying a second subset of theplurality of encoded signals associated with the first subset of theplurality of DS channels by the MIMO pre-coding matrix, and/or whereinthe processor is further configured to obtain second direct channelestimates of the plurality of DS channels at a first subcarrier, secondFEXT channel estimates within each of the plurality of DS MIMO groups atthe first subcarrier, and third FEXT channel estimates across theplurality of DS MIMO groups after performing the MIMO pre-coding andprior to performing the crosstalk pre-coding, wherein the second directchannel estimates and the second FEXT channel estimates are MIMOpost-coded channel estimates, generate a second DS channel matrixcomprising second diagonal entries representing the second directchannel estimates, second diagonal blocks each comprising secondoff-diagonal entries representing corresponding second FEXT channelestimates for each of the plurality of DS MIMO groups, and secondoff-diagonal blocks representing the third FEXT channel estimates,invert the second DS channel matrix to produce a FEXT pre-coding matrix,and perform the crosstalk pre-coding by multiplying the plurality ofencoded signals by the FEXT pre-coding matrix after performing the MIMOpre-coding, and/or further comprising a plurality of receivers coupledto the processor and configured to couple to the plurality of remote NEsvia a plurality of US channels, wherein the plurality of US channelsform a plurality of US MIMO groups, and receive a plurality of USsignals from the plurality of remote NEs via the plurality of USchannels at a second subcarrier, wherein the processor is furtherconfigured to perform crosstalk cancellation jointly on the plurality ofUS signals, and perform MIMO post-coding on the plurality of US signalsaccording to the plurality of US MIMO groups after performing thecrosstalk cancellation, and/or a first subset of the plurality of USchannels forms an i^(th) US MIMO group of the plurality of US MIMOgroups, wherein i is a positive integer, wherein the processor isfurther configured to obtain a US MIMO channel sub-matrix, denoted asH_(i,i), comprising diagonal entries representing direct channelestimates of the first subset of the plurality of US channels at thesecond subcarrier and off-diagonal entries representing FEXT channelestimates of the first subset of the plurality of US channels, decomposethe US MIMO channel sub-matrix H_(i,i) into a first matrix, denoted asA_(i,i) a second matrix, denoted as W_(i,i), and a third matrix, denotedas B_(i,i), where H_(i,i)=A_(i,i)×W_(i,i)×B_(i,i) ⁻¹; and perform theMIMO post-coding by multiplying a second subset of the plurality of USsignals associated with the first subset of the plurality of US channelsby a first inverse of the first matrix A_(i,i) ⁻¹and multiplying thesecond subset of the plurality of US signals by a second inverse of thesecond matrix W_(i,i) ⁻¹ after multiplying a second subset of theplurality of US signals associated with the first subset of theplurality of US channels by the first inverse of the first matrixA_(i,i) ⁻¹, and wherein the transmitter is further configured to sendthe third matrix B_(i,i) to corresponding remote NEs to facilitate MIMOpre-coding in a US direction, and/or wherein the processor is furtherconfigured to obtain second direct channel estimates of the plurality ofUS channels at the second subcarrier, second FEXT channel estimateswithin each of the plurality of US MIMO groups at the second subcarrier,and third FEXT channel estimates across the plurality of US MIMO groupsafter performing the MIMO pre-coding and prior to performing thecrosstalk pre-coding, wherein the second direct channel estimates andthe second FEXT channel estimates are MIMO pre-coded and MIMO post-codedchannel estimates, generate a second US channel matrix comprising seconddiagonal entries representing the second direct channel estimates,second diagonal blocks each comprising second off-diagonal entriesrepresenting corresponding second FEXT channel estimates for each of theplurality of US MIMO groups, and second off-diagonal blocks representingthe third FEXT channel estimates, invert the second US channel matrix toproduce a FEXT cancellation matrix, and perform the crosstalkcancellation by multiplying the plurality of US signals by the FEXTcancellation matrix.

In yet another embodiment, the disclosure includes a DSL remote-sideapparatus, comprising a plurality of receivers configured to receive aplurality of DS signals from a DSL office-side apparatus via a subset ofa plurality of DS channels forming a DS MIMO group, wherein theplurality of DS signals are pre-coded according to a DS MIMO pre-codingmatrix associated with the DS MIMO group at a first subcarrier andaccording to a DS FEXT pre-coding matrix associated with DS FEXTchannels of the plurality of DS channels at the first subcarrier, and aprocessor coupled to the plurality of receivers and configured toperform MIMO post-coding on the plurality of DS signals according to aDS MIMO post-coding matrix associated with the DS MIMO group. In someembodiments, the disclosure also includes further comprisingtransmitters coupled to the processor and configured to send the DS MIMOpre-coding matrix to the DSL office-side apparatus to facilitate MIMOpre-coding in a DS direction, wherein the processor is further configureto obtain a DS MIMO channel sub-matrix, denoted as H_(i,i), comprisingdiagonal entries representing first direct channel estimates of theplurality of DS channels at the first subcarrier and off-diagonalentries representing FEXT channel estimates of the plurality of DSchannels, decompose the DS MIMO channel sub-matrix H_(i,i) into a firstmatrix, denoted as A_(i,i), a second matrix, denoted as W_(i,i), and athird matrix, denoted as B_(i,i), where H_(i,i)=A_(i,i)×W_(i,i)×B_(i,i)⁻¹, wherein the DS MIMO pre-coding matrix corresponds to the thirdmatrix, and wherein the DS MIMO post-coding matrix is expressed asW_(i,i) ⁻¹×A_(i,i) ⁻¹, and perform the MIMO post-coding by multiplyingthe plurality of DS signals by a first inverse of the first matrixA_(i,i) ⁻¹, and multiplying the plurality of DS signals by a secondinverse of the second matrix W_(i,i) ⁻¹ after multiplying the pluralityof DS signals by the first inverse of the first matrix A_(i,i) ⁻¹,and/or wherein the receivers are further configured to receive a US MIMOpre-coding matrix, wherein the processor is further configured to obtaina plurality of encoded signals associated with a plurality of USchannels forming a US MIMO group at a second subcarrier, and multiplythe plurality of encoded signals by the US MIMO pre-coding matrix toproduce a plurality of output signals, wherein the DSL remote-sideapparatus further comprises a plurality of transmitters coupled to theprocessor and configured to transmit the plurality of output signals tothe DSL office-side apparatus via the plurality of US channels at thesecond subcarrier, and wherein the US MIMO pre-coding matrix isdecomposed from a US MIMO channel sub-matrix comprising diagonal entriesrepresenting direct channels of the plurality of US channels at thesecond subcarrier and off-diagonal entries representing US FEXT channelsof the plurality of US channels at the second subcarrier.

For the purpose of clarity, any one of the foregoing embodiments may becombined with any one or more of the other foregoing embodiments tocreate a new embodiment within the scope of the present disclosure.

These and other features will be more clearly understood from thefollowing detailed description taken in conjunction with theaccompanying drawings and claims.

BRIEF DESCRIPTION OF THE DRAWINGS

For a more complete understanding of this disclosure, reference is nowmade to the following brief description, taken in connection with theaccompanying drawings and detailed description, wherein like referencenumerals represent like parts.

FIG. 1 is a schematic diagram of an embodiment of a DSL system.

FIG. 2 is a schematic diagram of an embodiment of a vectored DSL system.

FIG. 3 is a schematic diagram of an embodiment of a MIMO DSL system.

FIG. 4 is a schematic diagram of an embodiment of a MU-MIMO DSL system.

FIGS. 5A and 5B illustrate an embodiment of copper wire pairconfigurations used to create three channels from two pairs of copperwires.

FIG. 6 is a schematic diagram of an embodiment of a MU-MIMO DSL systemin a DS direction.

FIG. 7 is a schematic diagram of an embodiment of a MU-MIMO DSL systemin a US direction.

FIG. 8 is a flowchart of an embodiment of a method of performing DSMU-MIMO DSL processing.

FIG. 9 is a flowchart of an embodiment of a method of performing USMU-MIMO DSL processing.

FIG. 10 is a flowchart of an embodiment of a method of determiningMU-MIMO matrix coefficients for a MU-MIMO DSL system.

FIG. 11 is a flowchart of an embodiment of a method of determining FEXTmitigation matrix coefficients for a MU-MIMO DSL system.

FIG. 12 is a flowchart of another embodiment of a method of determiningFEXT mitigation matrix coefficients for a MU-MIMO DSL system.

FIG. 13 is a flowchart of another embodiment of a method of performingDS MU-MIMO DSL processing.

FIG. 14 is a flowchart of another embodiment of a method of performingUS MU-MIMO DSL processing.

FIG. 15 is a schematic diagram of an embodiment of a NE.

DETAILED DESCRIPTION

It should be understood at the outset that although an illustrativeimplementation of one or more embodiments are provided below, thedisclosed systems and/or methods may be implemented using any number oftechniques, whether currently known or in existence. The disclosureshould in no way be limited to the illustrative implementations,drawings, and techniques illustrated below, including the exemplarydesigns and implementations illustrated and described herein, but may bemodified within the scope of the appended claims along with their fullscope of equivalents.

FIG. 1 is a schematic diagram of an embodiment of a DSL system 100. Thesystem 100 may be any DSL system as defined by the ITU-T. The system 100comprises a distribution point unit (DPU) 110 coupled to a plurality ofCPEs 130 via a plurality of subscriber lines 121, where at least some ofthe subscriber lines 121 are bundled in a cable binder 120. The DPU 110is located at an operator end of the system 100 such as a CO, anexchange, a cabinet, or a distribution point, which is connected to abackbone network such as the Internet via one or more intermediatenetworks. The intermediate networks may include an optical distributionnetwork (ODN). The CPEs 130 are shown as CPE 1 to CPE K and are locatedat distributed customer premises or subscriber locations and may befurther connected to devices such as telephones, routers, and computers.The subscriber lines 121 are twisted or untwisted copper pairs shown asline 1 to line K. The system 100 may be configured as shown oralternatively configured as determined by a person of ordinary skill inthe art to achieve similar functionalities.

The DPU 110 is any device configured to communicate with the CPEs 130.The DPU 110 terminates and aggregates DSL signals from the CPEs 130 andhands the aggregated DSL signals off to other network transports. In aDS direction, the DPU 110 forwards data received from a backbone networkto the CPEs 130. In a US direction, the DPU 110 forwards data receivedfrom the CPEs 130 onto the backbone network. The DPU 110 in someexamples comprises a plurality of xDSL office-side transceiver units(xTU-O) 111, where ‘x’ indicates any DSL standard. For instance, ‘x’stands for ‘A’ in ADSL2 or ADSL2+ systems, ‘V’ in VDSL or VDSL2 systems,and ‘F’ in G.fast systems. The xTU-Os 111 are shown as xTU-O₁ toxTU-O_(K). Each xTU-O 111 comprises a transmitter and a receiverconfigured to transmit and receive signals over a correspondingsubscriber line 121 using discrete multi-tone (DMT) modulation. DMTmodulation divides a signal spectrum of a subscriber line into a numberof discrete frequency bands and assigns a number of bits to eachfrequency band according to a channel condition of each frequency bandof the subscriber line. The frequency bands are also referred to astones or subcarriers.

In DMT modulation, a transmitter encodes data bits using forward errorcorrection (FEC) and maps the encoded data bits to quadratureamplitude-phase modulation (QAM) constellations. Each QAM constellationis mapped to a subcarrier. Thus, the QAM constellations are in afrequency domain. The transmitter performs inverse fast Fouriertransform (IFFT) to convert the frequency-domain QAM constellations intoa time-domain signal, which is referred to as a DMT symbol. Thetransmitter pre-appends a cyclic prefix (CP) to each DMT symbol to avoidinter-symbol-interference (ISI) and inter-carrier-interference (ICI) ata receiver. The transmitter transmits DMT signals carryingCP-pre-appended DMT symbols to a corresponding receiver at the CPEs 130.

Upon receiving a DMT signal, a receiver searches for the beginning of aDMT symbol, discards the CP, and performs fast Fourier transform (FFT)to convert the DMT symbol to a frequency-domain signal. The receivermultiplies the frequency-domain signal by a frequency-domain equalizer(FEQ) sample by sample. For example, FEQ coefficients may be single-tapcomplex values per FFT output or tone. The receiver performs FECdecoding on the demodulated and equalized signal to recover the originaldata bits transmitted by a DMT transmitter.

The DPU 110 may further comprise other functional units for performingphysical (PHY) layer signal processing, open system interconnection(OSI) model layer 2 (L2) and above (L2+) processing, activations of theCPEs 130, resource allocation, and other functions associated with themanagement of the system 100.

The CPEs 130 are any devices configured to communicate with the DPU 110.The CPEs 130 act as intermediaries between the DPU 110 and connecteddevices to provide Internet access to the connected devices. In a DSdirection, the CPEs 130 forward data received from the DPU 110 tocorresponding connected devices. In a US direction, the CPEs 130 forwarddata received from the connected devices to the DPU 110. Each CPE 130comprises an xDSL remote-side transceiver unit (xTU-R) 131. The xTU-Rs131 are shown as xTU-R₁ to xTU-R_(K). Each xTU-R 131 comprises areceiver and a transmitter configured to transmit and receive signalsover a corresponding subscriber line 121 using DMT modulation. The CPEs130 may further comprise other functional units for performing PHY layerprocessing and other management related functions.

In the system 100, the DPU 110 and the CPEs 130 negotiate configurationparameters for data transmission in both US and DS directions during aphase known as initialization or training, before transmissions ofinformation data during a phase known as showtime. US refers to thetransmission direction from the CPEs 130 to the DPU 110, whereas DSrefers to the transmission direction from the DPU 110 to the CPEs 130.Some examples of configuration parameters are channel information andbit allocations. Channel information is associated with channelconditions of the subscriber lines 121 at different tones. Bitallocation may include a number of bits to be allocated or loaded ateach frequency tone of a DMT symbol based on the channel conditions.

The system 100 may experience various interferences, such as near-endcrosstalk (NEXT) and FEXT. NEXT refers to the interference that occursat a receiver from a transmitter located at the same end of a cable suchas the subscriber lines 121 within a cable binder 120 from which asignal was transmitted. FEXT refers to the interference that propagatesdown and occurs at the opposite (far) end of a cable. In one embodiment,the system 100 employs frequency-division duplexing (FDD) tosimultaneously transmit US and DS signals in different frequency bandsto avoid NEXT. In FIG. 1, the solid arrows represent direct channelsfrom a given xTU-O 111 to a corresponding xTU-R 131 and the dashedarrows represent FEXT channels between the xTU-Os 111 and the xTU-Rs131. In such an embodiment, a timing advance technique is used tosynchronize all transmissions in the system 100 and to orthogonalizereceived signals and echoes of transmitted signals to avoid NEXTspectral leakage into the receiver. When transmissions in each US and DSdirection are synchronized among the subscriber lines 121, NEXT isorthogonal to the received signal in each direction. In anotherembodiment, the system 100 employs time-division duplexing (TDD) totransmit US and DS signals at different time slots, which removes theeffect of NEXT. However, FEXT remains in the system 100 whether thesystem 100 operates in a FDD mode or a TDD mode. In addition, FEXTcoupling among the subscriber lines 121 increases as the frequencyincreases, and thus may degrade system performance both in terms of datarate and stability.

FIG. 2 is a schematic diagram of a vectored DSL system 200. The system200 is similar to the system 100, but performs vectoring as described in“Self-FEXT Cancellation (Vectoring) for use with VDSL2 transceivers,”ITU-T document G.993.5 (G.vector), January 2010, which is incorporatedby reference, and the ITU-T document G.9701. Vectoring is a techniquethat coordinates signals among a group of lines such as the subscriberlines 121 to reduce the level of FEXT so that system performance may beimproved. The system 200 comprises a vector engine (VE) 212, a pluralityof xTU-Os 211 similar to the xTU-Os 111, and a plurality of xTU-Rs 231similar to the xTU-Rs 131. The xTU-Os 211 are coupled to the XTU-Rs 231via subscriber lines 221 similar to the subscriber lines 121 bundled ina cable binder 220 similar to the cable binder 120. The xTU-Os 211 areshown as xTU-O₁ to xTU-O_(K) and are collocated at a DPU 210 similar tothe DPU 110. The VE 212 is located at the DPU 210 and coupled to thexTU-Os 211. The xTU-Rs 231 are shown as xTU-R₁ to xTU-R_(K) and arelocated at different residences 230. The residences 230 are alsoreferred to as subscriber locations or customer premises or users. Thecollocated xTU-Os 211 and the non-collocated xTU-Rs 231 form a vectoredgroup 240. The solid arrows represent direct channels from a given xTU-O211 to a corresponding xTU-R 231. The dashed arrows represent FEXTchannels between the xTU-Os 211 and the xTU-Rs 231. The VE 212 isconfigured to perform FEXT cancellation both in the DS and USdirections. FEXT cancellation in the DS direction is performed by a FEXTprecoder.

When all the transmitters of the xTU-Os 211 are synchronized, each DStone received at an xTU-R 231 experiences FEXT only from the same toneof adjacent lines. Similarly, when all transmitters of the xTU-Rs 231are synchronized, each US tone received at an xTU-O 211 experiences FEXTonly from the same tone of adjacent lines. Thus, a frequency-domainchannel matrix may be defined, per tone, for each DS and US directionsas follows:

$\begin{matrix}{H_{c} = \begin{bmatrix}h_{11} & h_{12} & \ldots & h_{1K} \\h_{21} & h_{22} & \ldots & h_{2K} \\\ldots & \ldots & \ldots & \ldots \\h_{K\; 1} & h_{K\; 2} & \ldots & h_{KK}\end{bmatrix}} & (1)\end{matrix}$

where the diagonal elements h represent direct channels between a givenxTU-O 211 and a corresponding xTU-R 231. The off-diagonal elements h,where i j, represents FEXT channels and refers to the channel from aj^(th) transmitter into an i^(th) receiver. All elements h_(ij) arecomplex scalar values for 1≤i≤K and 1≤j≤K. It should be noted that thereis a different channel matrix for each tone, and there are differentchannel matrices for the DS FEXT channels as seen at the xTU-Rs 231 andfor the US FEXT channels as seen at the xTU-Os 211.

The ITU-T documents G.vector and G.fast describe procedures to performvectoring and estimation of the channel matrices H_(c). During atraining or initialization phase, the xTU-Os 211 transmit DS trainingsignals in the DS direction and each i^(th) xTU-R 231 estimates andcomputes DS h_(i,j) for 1≤j≤K and for all DS tones from the received DStraining signals. The xTU-Rs 231 send the DS h_(i,j) estimates to thexTU-Os 211 via a backchannel defined in the standard. After receivingall the DS h_(i,j) estimates, the xTU-Os 211 provide the DS h_(i,j)estimates to the VE 212 and the VE 212 constructs a DS channel matrix asshown in equation (1) for each DS tone according to the received DSh_(i,j) estimates. Similarly, the xTU-Rs 231 transmit US trainingsignals in the US direction during a training or initialization phaseand the xTU-Os 211 estimate and compute US h_(i,j) for 1≤j≤K and for allUS tones from the received US training signals. After obtaining all theUS h_(i,j) estimates, the xTU-Os 211 provides the US h_(i,j) estimatesto the VE 212 and the VE 212 constructs a US channel matrix as shown inequation (1) for each US tone according to the US h_(i,j) estimates.Subsequently, the VE 212 performs per-tone DS FEXT pre-coding based oncorresponding DS channel matrices and per-tone US FEXT cancellationbased on corresponding US channel matrices.

As shown in the system 200, the xTU-Os 211 are collocated, but thexTU-Rs 231 are not collocated. As such, coordination for FEXT processingis only performed at the collocated xTU-Os 211, but not at thenon-collocated xTU-Rs 231. Thus, in terms of FEXT, the system 200 maynot perform more than cancelling and eliminating the undesirable FEXT.However, in some DSL deployments such as G.fast deployments, at leastone subscriber residence may comprise two or more subscriber linesconnecting to a CO or a DPU. Therefore, at least some xTU-Rs arecollocated at a single subscriber residence. The collocation of at leastsome xTU-Rs in addition to the collocated xTU-Os may allow for moreadvanced signal processing techniques such as MIMO processing to furtherimprove system performance under FEXT.

In a MIMO system, all xTU-Rs are collocated. In this case, becausecoordination may be performed at both a DPU and a subscriber orresidence location, MIMO signal processing may be used to utilize FEXTrather than cancelling FEXT. When the FEXT signal is strong, MIMOprocessing may significantly enhance performance, for example, a signalenhancement by a few decibels (dB). Strong FEXT occurs on DSL lines athigher frequencies (e.g., higher than 50-100 MHz).

A MIMO system may use a SVD method or variations of SVD with pre-coderand post-coder or post-filter matrices that are unitary matrices andconserve power. In addition, such MIMO system gains from channeldiversity because FEXT signal from a transmitter to another receiver isexploited rather than mitigated. When N copper wire pairs are providedto a single subscriber, where N is a positive integer, alternative modesor phantom modes may be used in addition to regular differential modes.With N copper wire pairs, N differential and N−1 phantom modes areavailable, thus increasing the number of available channels to 2N−1. Assuch, alternative modes and phantom modes significantly increase thechannel capacity between a DPU and a subscriber, as described more fullybelow.

MIMO processing is commonly used in wireless systems to gain channeldiversity. A dedicated frequency band is used between a base station anda mobile station each having multiple antennas. N transmit antennas andN receive antennas create a MIMO system with a N×N channel matrix. Awireless system with M mobile stations each having N antennascommunicating with a base station having M times N transmit antennaswithin the same frequency band is a MU-MIMO system. Interference withineach MIMO group may be utilized while the interference across the MIMOgroups has to be mitigated. A similar MU-MIMO system in DSL is a DSLsystem, where at least one subscriber is served by two or more lines.

MU-MIMO processing is commonly used in wireless communication systems togain channel diversity as described in Lai-U Choi and Ross D. Murch, “Atransmit Preprocessing Technique for Multiuser MIMO Systems Using aDecomposition Approach,” Institute of Electrical and ElectronicsEngineers (IEEE) Transactions on Wireless Communications, Vol. 3, No. 1,January 2004 (Choi) and Quentin H. Spencer, A. Lee Swindlehurst, andMartin Haardt, “Zero-Forcing Methods for Downlink Spatial Multiplexingin Multiuser MIMO Channels,” IEEE Transactions on Signal Processing,Vol. 52, No. 2, February 2004 (Spencer), which are incorporated byreference. The methods of Choi and Spencer are computationally intensivedue to block diagonalization of a large channel matrix. Keke Zu, et al.,“Generalized Design of Low-Complexity Block Diagonalization TypePrecoding Algorithms for Multiuser MIMO Systems,” IEEE TRANSACTION ONCOMM., VOL. 61, No. 10, October 2013 (Zu) describes a lattice reductionaided simplified generalized minimum mean squared error channelinversion (LR-S-GMI-MMSE) method to reduce MIMO computational complexitywhen compared to Spencer's method. However, the LR-S-GMI-MMSE methodonly applies to transmit pre-coding, but not receive post-coding. Thus,the LR-S-GMI-MMSE method may be applied for DS only and not US andtherefore may not be suitable for implementation in DSL systems.

Disclosed herein are various embodiments for utilizing FEXT within agroup of MIMO channels while precoding and cancelling FEXT across MIMOgroups. The disclosed embodiments are suitable for use in a DSL systemthat comprises collocated xTU-Os coupled to at least some collocatedxTU-Rs. The xTU-Rs located at the same residence and correspondingxTU-Os form a MIMO group. In a DS direction, the collocated xTU-Osperform MIMO pre-coding and the collocated xTU-Rs perform MIMOpost-coding to utilize FEXT among MIMO channels within a MIMO group. Thecollocated xTU-Os perform FEXT pre-coding to cancel FEXT across the MIMOgroups. Similarly, in a US direction, the collocated xTU-Rs perform MIMOpre-coding and the collocated xTU-Os perform MIMO post-coding to utilizeFEXT among MIMO channels within a MIMO group. The collocated xTU-Osperform FEXT cancellation to cancel FEXT across the MIMO groups. In eachof the US and DS directions, the disclosed embodiments first diagonalizeeach MIMO group channel sub-matrix or block separately and determineMIMO pre-coding and post-coding matrices based on the matrixdiagonalization. After determining the MIMO pre-coding and MIMOpost-coding matrices, the disclosed embodiments determine a FEXTpre-coding matrix for the DS direction and a FEXT cancellation matrixfor the US direction to mitigate FEXT across the MIMO groups. Thedisclosed embodiments are computationally efficient since matrixdiagonalizations are applied to each MIMO group sub-channel matrixseparately instead of a complete channel matrix of all channels with alarger dimension. For example, in a DSL system with 5 MIMO groups eachhaving 2 pairs of lines, the disclosed embodiments reduce computationalcomplexity by about 18 times and about 2.5 times when compared to theSpencer and the LR-S-GMI-MMSE methods, respectively, while havingcomparable performance to Spencer's method and better performance thanLR-S-GMI-MMSE method.

FIG. 3 is a schematic diagram of an embodiment of a MIMO DSL system 300.The system 300 is similar to the MIMO DSL system described in G Taubockand W Henkel, “MIMO systems in the subscriber-line network,” 5thInternational OFDM Workshop, 2000, which is incorporated by reference.Unlike the systems 100 and 200, the system 300 serves a plurality ofxTU-Rs 321 similar to the xTU-Rs 131 and 231 collocated at a singleresidence 320. The system 300 comprises a plurality of xTU-Os 311similar to the xTU-Os 111 and 211 and further comprise a plurality ofxTU-Rs 321 similar to the xTU-Rs 231. The xTU-Os 311 are coupled to theXTU-Rs 321 via subscriber lines similar to the subscriber lines 121bundled in a cable binder similar to the cable binder 120. The xTU-Os311 are shown as xTU-O₁ to xTU-O_(K) and collocated at a DPU 310 similarto the DPUs 110 and 210. The xTU-Rs 321 are shown as xTU-R₁ toxTU-R_(K). The solid lines represent direct channels from a given xTU-O311 to a corresponding xTU-R 321. The dashed lines represent FEXTchannels between the xTU-Os 311 and the xTU-Rs 321. The system 300experiences similar FEXT as in the system 200. However, the collocationof the xTU-Os 311 and the collocation of the xTU-Rs 321 enable the useof MIMO processing at both the xTU-Os 311 and the xTU-Rs 321 to utilizethe FEXT instead of cancelling the FEXT, as described more fully. Thecollocated XTU-Os 311 and the collocated xTU-Rs 321 are referred to as aMIMO group 330. The channels h_(ij) for 1≤i≤K and 1≤j≤K within a MIMOgroup 330 are referred to as MIMO channels. FEXT among adjacentsubscriber lines are typically stronger at high frequencies such asabove 50 MHz to 100 MHz. When FEXT is strong, MIMO processing maysignificantly improve system performance, for example, by a few decibels(dBs). It should be noted that MIMO processing may be used inconjunction with vectoring-based FEXT cancellation, as described morefully below.

FIG. 4 is a schematic diagram of an embodiment of a MU-MIMO DSL system400. The system 400 is similar to the system 300, but serves multipleresidences 430 and 440 each having multiple subscriber lines similar tothe subscriber lines 121. The system 400 comprises a plurality of xTU-Os411 similar to the xTU-Os 111, 211, and 311 and a plurality of xTU-Rs421 similar to the xTU-Rs 131, 231, and 321. The xTU-Os 411 arecollocated at a DPU 410 similar to the DPUs 110, 210, and 310. A firstgroup of xTU-Rs 421 shown as xTU-R₁ to xTU-R_(m) are collocated at afirst residence 430 each served by a corresponding xTU-O 411 shown asxTU-O₁ to xTU-O_(m). Thus, the first group of xTU-Rs 421 andcorresponding xTU-Os 411 form a MIMO group 450 comprising m number ofchannels. A second group of xTU-Rs 421 shown as xTU-R_(m+1) toxTU-R_(m+n) are collocated at a second residence 440 each served by acorresponding xTU-O 411 shown as xTU-O_(m+1) to xTU-O_(m+n). Similarly,the second group of xTU-Rs 421 and corresponding xTU-Os 411 form a MIMOgroup 460 comprising n number of channels. To keep FIG. 4 simple andunderstandable not all the interconnection of FEXT channels are shown bydashed lines. However, every xTU-O 411 is connected to every xTU-R 421.FEXT within a MIMO group is typically stronger than FEXT across MIMOgroups. Therefore, utilizing FEXT within a MIMO group rather thancancelling the FEXT may improve system performance, as described morefully below. It should be noted that the system 400 may further compriseadditional collocated and/or non-collocated xTU-Rs similar to the xTU-Rs421.

FIGS. 5A and 5B illustrate an embodiment of copper wire pairconfigurations 500 and 510 used to create three channels from two pairsof copper wires. The configurations 500 and 510 may be employed by thesystems 100, 200, 300, and 400. Each pair of copper wires corresponds toa subscriber line 121. Most residences and businesses in the UnitedStates and some other countries are connected by two or more copperpairs to the so-called “service terminal” or “pedestals,” even thoughonly one pair may be active. Using two pairs, three channels areavailable. In general, with N-pairs, there are 2N wires. Assuming onewire is used as a reference or common ground, there are 2N−1 channelsavailable. As shown in FIGS. 5A and 5B, there are different ways ofcreating 2N−1 channels from N pairs. For example, 2N−1 channels may becreated from N pairs by keeping N differential modes (DM) and creatingN−1 alternative modes (AM) as shown in FIG. 5A for N=2. The alternativemodes are created by connecting the secondary of the couplingtransformers to one wire of each copper pair. In another method, Ndifferential modes and N−1 phantom modes (PM) are created. The phantommode is a differential mode channel created from the common modes of thetwo copper pairs as shown in FIG. 5B. In FIG. 5B, the center-taps of thesecondary of the coupling transformers are used to create the phantommode (PM1). N−1 phantom modes may be created from N pairs, for N>2,similar to the methods shown in FIGS. 5A and 5B. The FEXT egress andingress level of alternative or phantom modes into differential mode andother alternative or phantom modes in practical cables are high.However, MIMO processing may utilize the strong FEXT and gain channeldiversity to improve system performance as described more fully below.Since N wire pairs (lines) may represent 2N−1 channels, the followingembodiments describe MIMO processing and FEXT mitigation in terms ofchannels instead of lines.

FIG. 6 is a schematic diagram of an embodiment of a MU-MIMO DSL system600 in a DS direction. The system 600 is similar to the system 400 andillustrates a detailed view of MU-MIMO processing at collocated xTU-Os411 and the collocated xTU-Rs 421 and a detailed view of vectored-FEXTmitigation at the collocated xTU-Os 411. The system 600 comprises a DStransmitter 610 coupled to a plurality of DS receivers 630 via a cablebundle 620. The cable bundle 620 comprises subscriber lines similar tothe subscriber lines 121. The cable bundle 620 generates a plurality ofDS channels from the DS transmitter 610 to the DS receivers 630, wherethe DS channels serving a subscriber may be in differential modes onlyor in any of the configurations 500 and 510. The DS transmitter 610forms the transmitting portions of the collocated xTU-Os. Each DSreceiver 630 forms the receiving portions of the xTU-Rs collocated at asingle residence such as the residences 320, 430, and 440. The DStransmitter 610 comprises a plurality of MIMO pre-coders 611, a DS FEXTpre-coder 612, and a plurality of IFFT units 613. The MIMO pre-coders611 are shown as [V_(l,l)] to [V_(n,n)], which are representations ofMIMO pre-coding matrix coefficients, as described more fully below. EachDS receiver 630 comprises a plurality of FFT units 631, a plurality ofFEQs 632, a plurality of MIMO post-coders 633, and a plurality ofslicers 634. Each DS receiver 630 and a corresponding portion of the DStransmitter 610 form a MIMO group 640 similar to the MIMO groups 330,450, and 460. The MIMO post-coders 633 each comprising first sub-block635 coupled to a second sub-block 636. The first sub-blocks 635 areshown as [U_(l,l) ^(H)] to [U_(n,n) ^(H)] and the second sub-blocks 636are shown as [S_(l,l) ⁻¹] to [S_(n,n) ⁻¹], where [U_(l,l) ^(H)] to[U_(n,n) ^(H)] and [S_(l,l) ⁻¹] to [S_(n,n) ⁻], are representations ofMIMO post-coding matrix coefficients, as described more fully below.

The system 600 further comprises n number of MIMO groups 640. Forexample, each i^(th) MIMO group 640 comprises m_(i) number of channels.Then, the total number of channels, denoted as K, in the system 600 isshown as follows:

K=Σ _(i=1) ^(i=n) m _(i)   (2)

It should be noted that in order to apply MIMO processing, a systemhaving K channels may serve a maximum of K−1 users so that at least oneuser is served by more than one channel.

The DS transmitter 610 is configured to receive encoded signals carryingDS modulation symbols or frequency-domain constellations for the Kchannels, denoted as X₁ to X_(K). In a digital implementation, X₁ toX_(K) may be complex numbers. Each MIMO pre-coder 611 is configured tojointly pre-code the DS modulation symbols of all channels within acorresponding MIMO group 640 for MIMO processing. The K channels or then MIMO groups form a vectored group 650 similar to the vectored group240. The DS FEXT pre-coder 612 is coupled to the MIMO pre-coders 611 andconfigured to jointly pre-code all MIMO pre-coded symbols of all MIMOgroups 640 for vectored DS FEXT pre-compensation. The IFFT units 613 arecoupled to the DS FEXT pre-coder 612. The IFFT units 613 are configuredto perform IFFTs on m_(i) channel signals within a corresponding MIMOgroup 640. The operations of the MIMO pre-coders 611 and the DS FEXTpre-coder 612 are described more fully below.

The DS receivers 630 are configured to receive signals transmitted bythe DS transmitter 610. Each DS receiver 630 receives and processessignals for m_(i) channels within a corresponding MIMO group 640. Ateach DS receiver 630, the FFT units 631 are coupled to the FEQs 632, theFEQs 632 are coupled to MIMO post-coders 633, and the MIMO post-coders633 are coupled to the slicers 634. The FFT units 631 are configured toperform FFTs on the m_(i) channel signals within a corresponding MIMOgroup 640. The FEQs 632 are configured to perform frequency-domainchannel equalization on the m_(i) channel signals within a correspondingMIMO group 640. Each MIMO post-coder 633 is configured to perform MIMOpost-coding on the m_(i) channel signals within a corresponding MIMOgroup 640. In an embodiment, for each line i, the FEQs 632 may beincluded in the MIMO post-coder 633's [S_(i,i) ⁻¹] . In such anembodiment, the FEQs 632 comprises FEQ coefficients with values of one.The slicers 634 are configured to recover the transmitted modulationsymbols or constellations X_(i)'s from the m_(i) channel signals withina corresponding MIMO group 640. The operations of the MIMO post-coders633 are described more fully below.

The MIMO pre-coders 611 and the MIMO post-coders 633 are determinedusing a matrix decomposition method such as singular-value decomposition(SVD). Assuming synchronization and vectoring, using DMT modulation withCPs long enough for ISI and ICI avoidance, the tones of the DMT areorthogonal to one another and therefore each tone may be processedindependently. A DS channel matrix H is defined to represent the DSchannels in the system 600 at a given tone as follows:

$\begin{matrix}{H = \begin{bmatrix}H_{1,1} & \ldots & H_{1,n} \\\vdots & \ddots & \vdots \\H_{n,1} & \ldots & H_{n,n}\end{bmatrix}} & (3)\end{matrix}$

where each component H_(i,j) for 1≤i≤n and 1≤j≤n is a sub-matrix of sizem_(i) by m_(j) as shown below:

$\begin{matrix}{{H_{i,j} = \begin{bmatrix}h_{i_{1},j_{1}} & \ldots & h_{i_{1},j_{m_{j}}} \\\vdots & \ddots & \vdots \\h_{i_{m_{i}},j_{1}} & \ldots & h_{i_{m_{i}},j_{m_{j}}}\end{bmatrix}_{m_{i} \times m_{j}}},{\forall i},j} & (4)\end{matrix}$

where m_(i) is the number of channels or lines in an i^(th) MIMO group640 and ∀ represents all values of i and j, for example, 1≤i≤n and1≤j≤n. The diagonal blocks of H, H_(i,i), ∀i each represents MIMOchannels for an i^(th) MIMO group 640, where the MIMO channels includeintra-crosstalk and direct channels of lines within an i^(th) MIMO group640. The diagonal blocks are also referred to as MIMO channelsub-matrices. The off-diagonal blocks of H_(i,j), i≠j each representsinter-MIMO crosstalk channels between an i^(th) MIMO group 640 and aj^(th) MIMO group 640.

SVD is applied to each MIMO channel sub-matrix H_(i,i) as follows:

H _(i,i) =U _(i,i) ×S _(i,i) ×V _(i,j) ^(H) , ∀i   (5)

where U_(i,i) and V_(i,i) are unitary matrices that preserve powerS_(i,i) is a diagonal matrix, and the superscript H represents aconjugate transpose operation.

A DS MIMO channel matrix H_(M) is defined to represent the MIMO channelsub-matrices H_(i,i) of all MIMO groups 640 as follows:

$\begin{matrix}{H_{M} = \begin{bmatrix}H_{1,1} & \ldots & 0 \\\vdots & \ddots & \; \\0 & \ldots & H_{n,n}\end{bmatrix}} & (6)\end{matrix}$

and the matrices U_(i,i), V_(i,i) and S_(i), are obtained from SVD asshown below:

$\begin{matrix}{{U = \begin{bmatrix}U_{1,1} & \ldots & 0 \\\vdots & \ddots & \; \\0 & \ldots & U_{n,n}\end{bmatrix}},{S = \begin{bmatrix}S_{1,1} & \ldots & 0 \\\vdots & \ddots & \; \\0 & \ldots & S_{n,n}\end{bmatrix}},{V = \begin{bmatrix}V_{1,1} & \ldots & 0 \\\vdots & \ddots & \; \\0 & \ldots & V_{n,n}\end{bmatrix}}} & (7)\end{matrix}$

The matrix V is used to construct the MIMO pre-coders 611 at the DStransmitter 610. Each MIMO pre-coder 611 multiplies the encoded signalsor DS modulation symbols by a corresponding V_(i,j). The matrices S andU are used to construct the MIMO post-coders 633. Each MIMO post-coder633 multiplies corresponding FEQ 632 output signals by S_(i,j)⁻¹×U_(i,i) ^(H), where the superscript −1 represents a matrix inverseoperation. This multiplication of FEQ 632 output signals by S_(i,i)⁻¹×U_(i,i) ^(H) is equivalent to multiplying FEQ 632 output signals byU_(i,i) ^(H) followed by a multiplication by S_(i,i) ⁻¹.

The DS FEXT pre-coder 612 is constructed from a DS FEXT pre-codingmatrix, denoted as P, where the DS FEXT pre-coder 612 multiples the MIMOpre-coder 611 output signals of all MIMO groups 640 by the DS FEXTpre-coding matrix P. In order for signals received at the DS receivers630 to be equal to signals transmitted by the DS transmitter 610,operations performed by the MIMO pre-coders 611, the DS FEXT pre-coder612, and the MIMO post-coders 633 and the channels generated by thecable bundle 620 satisfy the following condition:

S ⁻¹ ×U ^(H) ×H×P×V=I _(K×K)   (8)

where I_(K×K) is an identity matrix. Thus, the DS FEXT pre-coding matrixP is expressed as shown below:

$\begin{matrix}\begin{matrix}{P = {( {{S^{- 1} \cdot U^{H}} \times H} )^{- 1} \times V^{- 1}}} \\{= {H^{- 1} \times H_{M}}}\end{matrix} & (9)\end{matrix}$

It should be noted that equations (8) and (9) do not account for noisein the channels.

The end-to-end model of the system 600 is shown below:

Y=S ⁻¹ ×U ^(H)×(H×P×V×X+F×N)   (10)

where Y is a column vector [Y₁, Y₂, . . . Y_(K)] representing outputs atthe slicers 634, X is a column vector [X₁, X₂, . . . X_(K)] representinginputs at the DS transmitter 610, F represents FEQ coefficients of theFEQs 632, and N represents additive white Gaussian noise (AWGN).

The computation of the DS FEXT pre-coding matrix P as shown in equation(9) may be intensive when the number of channels K is large. In anembodiment, a two-step approach is used to reduce computationcomplexity. In the two-step approach, the channel matrix H shown inequation (3) is re-estimated after determining the MIMO pre-codingmatrices V_(i,i) and the MIMO post-coding matrices S_(i,i) ⁻¹U_(i,i)^(H) and applying the MIMO pre-coder 611 at the DS transmitter 610 andthe MIMO post-coders 633 at the DS receivers 630. To illustrate thereduced matrix P computation, K is set to a value of 8, indicating 8 DSchannels, and n is set to a value of 3, indicating 3 MIMO groups 640.For example, channels 1 to 3 form a first MIMO group 640, channels 4 and5 form a second MIMO group 640, channels 6 and 7 form a third MIMO group640, and channel 8 is single non-MIMO channel. The original channelmatrix H shown in equation (3) is rewritten as follows:

where m_(ij) for 1≤i≤3 and 1≤j≤3 represents direct channels andintra-crosstalk in the first MIMO group 640, n_(ij) for 4≤i≤5 and 4≤j≤5represent direct channels and intra-crosstalk in the second MIMO group640, I_(ij) for 6≤i≤7 and 6≤j≤7 represents direct channels andintra-crosstalk in the third MMO group 640, h₈₈ represents the directchannel for the last channel, and the remaining h_(ij) for 1≤i≤8 and1≤j≤8 represents FEXT channels across all the MIMO groups 640. Thedashed rectangles in equation (11) illustrate the three MIMO groups 640.

A MIMO channel sub-matrix is defined for each MIMO group 640 and SVD isapplied to each MIMO channel sub-matrix similar to equation (5) asfollows:

$\begin{matrix}{{M = {\begin{bmatrix}m_{11} & m_{12} & m_{13} \\m_{21} & m_{22} & m_{23} \\m_{31} & m_{32} & m_{33}\end{bmatrix} = {U_{M}S_{M}V_{M}^{H}}}}{N = {\begin{bmatrix}n_{44} & n_{45} \\n_{54} & n_{55}\end{bmatrix} = {U_{N}S_{N}V_{N}^{H}}}}{L = {\begin{bmatrix}l_{66} & l_{67} \\l_{76} & l_{77}\end{bmatrix} = {U_{L}S_{L}V_{L}^{H}}}}} & (12)\end{matrix}$

where M, N, and L represent the MIMO channel matrices of the first,second, and third MIMO groups 640, respectively. The MIMO pre-coders 611in the first, second, and third MIMO groups 640, multiply correspondingDS symbols by V_(M), V_(N), and V_(L), respectively. In the MIMOpost-coders 633 in the first, second, and third MIMO groups 640,multiply corresponding FEQs′ 632 output signals by S_(M) ⁻¹×U_(M) ^(H),S_(N) ⁻¹×U_(N) ^(H), and S_(L) ⁻¹×U_(L) ^(H), respectively.

After applying the MIMO pre-coders 611 and the MIMO post-coders 633, thechannel matrix His re-estimated while the xTU-Os and the xTU-Rs transmittraining signals using similar mechanisms described above. There-estimated channel matrix, denoted as H₂, is shown below:

where m′_(ij) for 1≤i≤3 and 1≤j≤3, n′_(ij) for 4≤i≤5 and 4≤j≤5, andl′_(ij) for 6≤i≤7 and 6≤j≤7 are re-estimated channels of the first,second, and third MIMO groups 640, and H_(ij) for 1≤i≤8 and 1≤j≤8 arere-estimated FEXT channels among the MIMO groups 640. As shown, thediagonal components of the MIMO channel sub-matrices M N, and L (e.g.,m′_(ij) for 1≤i≤3 and 1≤j≤3, n′_(ij) for 4≤i≤5 and 4≤j≤5, and l′_(ij)for 6≤i≤7 and 6≤j≤7) comprise values of 1 after applying MIMO pre-codingand the MIMO post-coding. The off-diagonal components of the MIMOchannel sub-matrices M N, and L (e.g., m′_(ij) for 1≤i≤3 and 1≤j≤3,n′_(ij) for 4≤i≤5 and 4≤j≤5, and l′_(ij) for 6≤i≤7 and 6≤j≤7) maycomprise values of zeros or close to zeros after applying MIMOpre-coding and the MIMO post-coding. The non-zero values are due tonoise or channel estimation error in 11 _(2.)

The DS FEXT pre-coding matrix P is recomputed by setting theoff-diagonal elements m′_(ij), n′_(ij), and l′_(ij), where i≠j, of theMIMO groups 640 to values of zeros and inverting the re-estimatedchannel matrix H₂ as follows:

P=H ₂ ⁻¹   (14)

Comparing equation (9) to equation (14), equation (14) is lesscomputationally intensive. It should be noted that equations (11) to(14) may be extended to include any number of channels and any number ofMIMO groups. In general, the diagonal blocks of H₂ are identity matricesand the off-diagonal blocks of H₂ are changed from the off-diagonalblocks of H.

In an embodiment, the DS receivers 630 compute channel estimates fordirect channels and FEXT channels in a DS direction (e.g., H_(i,j)),performs SVD to determine MIMO pre-coding matrices (e.g., V_(i,i)) andMIMO post-coding matrices (e.g., S_(i,i) ⁻¹×U_(i,i) ^(H)) according toequation (5), and sends the MIMO pre-coding matrices and the channelestimates to the DS transmitter 610. The DS transmitter 610 computes aFEXT pre-coding matrix (e.g., P) based on the channel estimates receivedfrom the DS receivers 630 according to equation (9) or (14).

FIG. 7 is a schematic diagram of an embodiment of a MU-MIMO DSL system700 in a US direction. The system 700 is similar to the system 400 andillustrates a detailed view of MIMO processing at collocated xTU-Os 411and the collocated xTU-Rs 421 and a detailed view of vectored-FEXTmitigation at the collocated xTU-Os 411. The system 700 comprises asimilar structure as the system 600. However, instead of performing FEXTpre-coding, the system 700 performs FEXT cancellation, since UStransmitters 730 are not collocated. The system 700 comprises a USreceiver 710 coupled to the US transmitters 730 via a cable bundle 720similar to the cable bundle 620. The cable bundle 720 generates aplurality of US channels from the US transmitters 730 to the US receiver710, where the US channels may be in differential mode or any of theconfigurations 500 and 510. The US receiver 710 forms the receivingportions of the collocated xTU-Os. Each US transmitter 730 forms thetransmitting portions of the xTU-Rs collocated at a single residencesuch as the residences 230, 320, 430, and 440.

The US receiver 710 comprises a plurality of slicers 711, a plurality ofMIMO post-coders 712, a US FEXT canceller 713, a plurality of FEQs 714,and a plurality of FFT units 715. The slicers 711, the FEQs 714, and theFFT units 715 are similar to the slicers 634, the FEQs 632, and the FFTunits 631, respectively. The MIMO post-coders 712 are similar to theMIMO post-coders 633 each comprising a first sub-block 717 similar tothe first sub-block 635 and a second sub-block 716 similar to the secondsub-block 636. The first sub-blocks 717 are shown as [U_(l,l) ^(H)] to[U_(n,n) ^(H)] and the second sub-blocks 716 are shown as [S_(l,l) ⁻¹]to [S_(n,n) ⁻¹]. The slicers 711, the MIMO post-coders 712, the FEQs714, and the FFT units 715 are arranged in a similar order as the DSreceivers 630. The additional US FEXT canceller 713 is positionedbetween the FEQs 714 and the MIMO post-coders 712. Each US transmitter730 comprises a plurality of IFFT units 731 similar to the IFFT units613 and MIMO pre-coders 732 similar to the MIMO pre-coders 611 and areshown as [V_(l,l)] to [V_(n,n)]. The IFFT units 731 and the MIMOpre-coders 732 are arranged in a similar order as the DS transmitter610. However, there is no US FEXT pre-coding at the non-collocated UStransmitters 730. Each US transmitter 730 and a corresponding portion ofthe US receiver 710 form a MIMO group 740 similar to the MIMO groups330, 450, 460, and 640. The US channels across all the MIMO groups 740to form a vectored group 750 similar to the vectored groups 240 and 650.The US FEXT canceller 713 is configured to perform vectored US FEXTcancellation on frequency-domain equalized signals output by the FEQs714.

A US channel matrix H similar to the DS channel matrix H shown inequation (3) is defined to represent the US channels in the system 700.The system 700 performs similar MIMO processing as the system 600 anddetermines MIMO pre-coding matrices for the MIMO pre-coders 732 and MIMOpost-coding matrices for the MIMO post-coders 712 using similarmechanisms as the system 600. A US MIMO channel matrix H_(M) is definedas shown in equation (6) and SVD is performed as shown in equation (5)to obtain unitary matrices U and V and diagonal matrix S as shown inequation (7). Each MIMO pre-coder 732 multiplies encoded signals or USmodulation symbols, denoted as X₁ to X_(K), by a corresponding V_(i,i).This operation for the entire MU-MIMO system is represented by V×X whereV is defined in equation (7). Each MIMO post-coder 712 multipliescorresponding US FEXT canceller 713 output signals, denoted as z₁ toz_(K), which forms a vector Z_(F), by S_(i,i) ⁻¹, U_(i,i) ^(H). Thisoperation for the entire MU-MIMO system is represented byS⁻¹×U^(H)×Z_(F), where S and U are defined in equation (7).

The US FEXT canceller 713 is constructed from a US FEXT cancellationmatrix, denoted as C, where the US FEXT canceller 713 multiples the FEQ714 output signals of all channels by the US FEXT cancellation matrix C.In order for signals recovered by the US receiver 710 to be equal tosignals transmitted by the US transmitters 730, operations performed bythe MIMO pre-coders 732, the US FEXT canceller 713, the MIMO post-coders712, and the US channels generated by the cable bundle 720 shouldsatisfy the following condition:

S ⁻¹ ×U ^(H) ×C×H×V=I _(K×K)   (15)

Thus, the US FEXT cancellation matrix C is expressed as shown below:

$\begin{matrix}\begin{matrix}{C = {U \times S \times V^{H} \times H^{- 1}}} \\{= {H_{M} \times H^{- 1}}}\end{matrix} & (16)\end{matrix}$

It should be noted equation (16) does not account for noise in thechannels.

The end-to-end model of the system 700 is shown below:

Y=S ⁻¹ ×U ^(H) ×C×(H×V×X+F×N)   (17)

where Y is a column vector [Y₁, Y₂, . . . Y_(K)] representing outputs atthe slicers 711, X is a column vector [X₁, X₂, . . . X_(K)] representinginputs at the US transmitters 730, F represents FEQ coefficients of theFEQs 714, and N represents AWGN noise.

In an embodiment, the two-step approach described above is applied toreduce computational complexity of the US FEXT cancellation matrix Cshown in equation (16). In such an embodiment, the US channel matrix Hisre-estimated after applying the MIMO pre-coders 732 and the MIMOpost-coders 712 as shown in equations (11) to (14). Thus, the US FEXTcancellation matrix C is computed as follows:

C=H ₂ ⁻¹   (18)

In an embodiment, the US receiver 710 computes channel estimates fordirect channels and FEXT channels in a US direction (e.g., H_(ij)),performs SVD to determine MIMO pre-coding matrices (e.g., V_(i,i)) andMIMO post-coding matrices (e.g., S_(i,i) ⁻¹×U_(i,i) ^(H)) according toequation (5), sends the MIMO pre-coding matrices to the US transmitter730, and computes a FEXT cancellation matrix (e.g., C) according toequation (16) or (18), and sends the MIMO pre-coding matrices to the UStransmitters 730.

In an embodiment, a MIMO DSL system such as the systems 300, 400, 600,and 700 uses a GMD method to determine matrix coefficients for MIMOpre-coders such as the MIMO pre-coders 611 and 732, MIMO post-coderssuch as the MIMO post-coders 633 and 712, DS FEXT pre-coders such as theDS FEXT pre-coder 612, and US FEXT cancellers such as the US FEXTcanceller 713. For example, the system comprises a plurality of channelsand a plurality of MIMO groups similar to the MIMO groups 330, 450, 460,640, and 740 formed from the plurality of channels. In such anembodiment, a channel matrix H is defined to represent channels, whichmay be US channels or DS channels, in the system similar to equation (3)and a MIMO channel sub-matrix H_(i,i) is defined to represent channelswithin a MIMO group similar to equation (4). Each MIMO channelsub-matrix H_(i,i) is decomposed using GMD as follows:

H _(i,i) =Q _(i,i) G _(i,i) T _(i,i) ^(H) , ∀i   (19)

where Q_(i,i) and T_(i,i) are matrices comprising orthonormal columns,and G_(i,i) is a real upper triangular matrix with diagonal entriesequal to the geometric mean of the positive singular values of H_(i,i).Similar to the SVD method, the transmitter of each MIMO group such asthe DS transmitter 610 and the US transmitters 730 performs MIMOpre-coding by multiplying encoded signals by T_(i,i), and the receiverof each MIMO group such as the DS receivers 630 and the US receiver 710performs MIMO post-coding by multiplying frequency-domain equalizedsignals by G_(i,j) ⁻¹×Q_(i,i) ^(H). The DS FEXT pre-coder matrix P iscomputed as shown in equations (9) or (14) and the US FEXT cancellermatrix C is computed as shown in equations (16) or (18). It should benoted that since G_(i,i) is a triangular matrix, the MIMO post-codingmay be implemented using a back substitution method to further reducecomputational complexity instead of directly computing G_(i,i) ⁻¹.

In another embodiment, a generalized matrix decomposition method is usedto compute the MIMO pre-coding matrices and the MIMO post-codingmatrices. For example, the MIMO channel sub-matrices are decomposed asfollows:

H _(i,i) =A _(i,i) ×W _(i,i) ×B _(i,i) ⁻¹ , ∀i   (20)

where A_(i,i), W_(i,i), and B_(i,i) are non-singular matrices. Thematrices A_(i,i), W_(i,i), and B_(i,i) may be selected such that matrixinversion may be easily performed. For example, the matrices A_(i,i) andB_(i,i) may be unitary matrices and W_(i,i) may be a diagonal matrix, atriangular matrix, or a Hessenberg matrix. Similar to the SVD and theGMD methods, the transmitter of each MIMO group such as the DStransmitter 610 and the US transmitters 730 performs MIMO pre-coding bymultiplying the transmitted signals by B_(i,i), and the receiver of eachMIMO group, such as the US receiver 710 and the DS receivers 630,performs MIMO post-coding by multiplying the received signals at FEQoutputs such as the FEQs 632 and 714 outputs by A_(i,i) ⁻¹ and followedby multiplying the results by W_(i,i) ⁻¹, ∀i. The DS FEXT pre-codermatrix P are computed as shown in equations (9) or (14) and US FEXTcanceller matrix C are computed as shown in equations (16) or (18).

In a first embodiment, the matrix W_(i,i) in equation (20) is an uppertriangular matrix with non-zero diagonal entries. In such an embodiment,a transmitter such as the DS transmitter 610 and the US transmitters730, applies a nonlinear approach, e.g., Tomlinson-Harashima precoding(THP), to the equation (20). For example, the matrix decomposition isfurther decomposed as follows:

H _(i,i)=(A _(i,i)×diag(W _(i,i)))×((diag(W _(i,i)))⁻¹ ×W _(i,i))×B_(i,i) ⁻¹ , ∀i   (21)

where diag(W_(i,i)) represents a diagonal matrix with diagonal entriesof W_(i,i). The term ((diag(W_(i,i))⁻¹×W_(i,i)) in equation (21) is anupper triangular matrix, which may be represented as {tilde over(W)}_(i,i), with diagonal entries comprising values of ones as shownbelow:

$\begin{matrix}{{\overset{\sim}{W}}_{i,i} = \begin{bmatrix}1 & w_{1,2} & \ldots & w_{1,m_{i}} \\0 & 1 & \ldots & w_{2,m_{i}} \\\ldots & \ldots & \ddots & \ldots \\0 & 0 & \ldots & 1\end{bmatrix}} & (22)\end{matrix}$

The nonlinear approach is formulated as y=N (x) defined by the matrix{tilde over (W)}_(i,i), where N represents a nonlinear function, yrepresents the output of the nonlinear function N, and x represents theinput to the nonlinear function N. The nonlinear approach may becomputed by selecting a positive bound as shown below:

u>2×max {|

{x ₁ }|,

{x ₁}|,

{x ₂}|, . . . , |

{x _(m) _(i) }|,

x_(m) _(i) }|,

{x_(m) _(i) }|}  (23)

where

{x₁} and

{x₁} represent the real and imaginary components of x₁, respectively.Subsequently, y may be computed iteratively from the last entry, denotedas y_(n), to the first entry, denoted as y₁, where 1, . . . , m_(i)represent sample indices, as shown below:

$\begin{matrix}{\mspace{79mu} {{y_{m_{i}} = x_{m_{i}}}\{ \begin{matrix}{{{\overset{\sim}{y}}_{j} = {x_{j} - {\sum\limits_{k = {j + 1}}^{m_{i}}{w_{j,k} \times y_{k}}}}},{j = {m_{i} - 1}},{m_{i} - 2},\ldots \mspace{14mu},1} \\{{y_{j} = {\lbrack {{- \frac{u}{2}} + {( {{\Re \{ {\overset{\sim}{y}}_{j} \}} + \frac{u}{2}} ){mod}\; u}} \rbrack + {\lbrack {{- \frac{u}{2}} + {( {{\{ {\overset{\sim}{y}}_{j} \}} + \frac{u}{2}} ){mod}\; u}} \rbrack \times \sqrt{- 1}}}},{j = {m_{i} - 1}},{m_{i} - 2},\ldots \mspace{14mu},1}\end{matrix} }} & (24)\end{matrix}$

where j and k represents sample indices, u represents the above selectedpositive bound, and amodu represents a modulo operation as shown below:

$\begin{matrix}{{a\mspace{11mu} {mod}\mspace{11mu} u} = {a - {u \times {{floor}( \frac{a}{u} )}}}} & (25)\end{matrix}$

When applying the equation (21), a transmitter performs MIMO pre-codingby applying the nonlinear approach described above in equations (23) and(24) to an input signal, for example, modulation symbols X₁ to X_(K), toproduce an intermediate signal, followed by multiplying the intermediatesignal by the matrix B_(i,i) to produce pre-coded signals. In thereceiver side, each MIMO group such as the US receiver 710 and the DSreceivers 630 performs MIMO post-coding by applying the modulo operationshown in equation (25) to received signals at FEQ (e.g., FEQs 632 and714) outputs, followed by multiplying the modulo operation outputsignals by (A_(i,i)×diag (W_(i,i)))⁻¹ (diag (W_(i,i)))⁻¹×A_(i,i) ⁻. Whenemploying the nonlinear approach, the DS FEXT pre-coder matrix P arecomputed as shown in equations (9) or (14) and US FEXT canceller matrixC are computed as shown in equations (16) or (18).

In a second embodiment, the matrix W_(i,i) in equation (21) is a lowertriangular matrix. In such an embodiment, {tilde over (W)}_(i,i) inequation (22) is as shown below:

$\begin{matrix}{{\overset{\sim}{W}}_{i,i} = \begin{bmatrix}1 & 0 & \ldots & 0 \\w_{2,1} & 1 & \ldots & 0 \\\ldots & \ldots & \ddots & \ldots \\w_{m_{i},1} & w_{m_{i},2} & \ldots & 1\end{bmatrix}} & (26)\end{matrix}$

Then the output of the nonlinear approach is obtained iteratively asfollows:

$\begin{matrix}{\mspace{79mu} {{y_{1} = x_{1}}\{ \begin{matrix}{{{\overset{\sim}{y}}_{j} = {x_{j} - {\sum\limits_{k = 1}^{j - 1}{w_{k,j} \times y_{k}}}}},{j = 2},3,\ldots \mspace{14mu},m_{i}} \\{{y_{j} = {\lbrack {{- \frac{u}{2}} + {( {{\Re \{ {\overset{\sim}{y}}_{j} \}} + \frac{u}{2}} ){mod}\; u}} \rbrack + {\lbrack {{- \frac{u}{2}} + {( {{\{ {\overset{\sim}{y}}_{j} \}} + \frac{u}{2}} ){mod}\; u}} \rbrack \times \sqrt{- 1}}}},{j = 2},3,\ldots \mspace{14mu},m_{i}}\end{matrix} }} & (27)\end{matrix}$

In a third embodiment, the matrix W_(i,i) in equation (21) is either anupper or a lower triangular matrix with non-zero diagonal entries. Insuch an embodiment, a receiver such as the DS receivers 630 and the USreceiver 710 applies a nonlinear approach, e.g., Generalized DecisionFeedback Equalization, for MIMO post-coding. A transmitter such as theDS transmitter 610 and the US transmitters 730 performs MIMO precodingby multiplying input signals by B_(i,i). In the receiver side, each MIMOgroup such as the US receiver 710 and the DS receivers 630 performs MIMOpost-coding by first multiplying the FEQ (e.g., FEQs 632 and 714) outputsignals by A_(i,i) ⁻¹ and then using W_(i,i) for decision feedbackequalization. The DS FEXT pre-coder matrix P is computed as shown inequations (9) or (14) and the US FEXT canceller matrix C is computed asshown in equations (16) or (18).

In yet another embodiment, a generalized matrix decomposition method isused to compute the MIMO pre-coding matrices and the MIMO post-codingmatrices. For example, the MIMO channel sub-matrices are decomposed asfollows:

H _(i,i) =A _(i,i) ×W _(i,i) ^(A) ×W _(i,i) ^(B) ×B _(i,i) ⁻¹ , ∀i  (28)

where A_(i,i), W_(i,i) ^(A), W_(i,i) ^(B), and B_(i,i) are non-singularmatrices, and the matrices W_(i,i) ^(A) and W_(i,i) ^(B) are anycombination of upper and lower triangular matrices with all diagonalentries equal to one. A nonlinear approach, e.g., Tomlinson-Harashimaprecoding (THP) may be applied at a transmitter such as the DStransmitter 610 and the US transmitters 730. A nonlinear approach, e.g.,Generalized Decision Feedback Equalization is applied at a receiver suchas the DS receivers 630 and US receiver 710. The transmitter side MIMOprecoding comprises using the nonlinear approach corresponding toW_(i,i) ^(B) to pre-code input signals and then uses the matrix B_(i,i)to pre-code the output signals of the nonlinear approach by multiplyingthe output signals by B _(i,i). In the receiver side, each MIMO groupsuch as the US receiver 710 and the DS receivers 630 performs MIMOpost-coding by first applying the modulo operation as shown in equation(25) to received signals at FEQ (e.g., FEQs 632 and 714) outputs, andthen multiplying the modulo operation output signals by A_(i,i) ⁻¹, andthen further using W_(i,i) ^(A) or decision feedback equalization. TheDS FEXT pre-coder matrix P is computed as shown in equations (9) or (14)and the US FEXT canceller matrix C is computed as shown in equations(16) or (18).

FIG. 8 is a flowchart of an embodiment of a method 800 of performing DSMU-MIMO DSL processing. The method 800 is implemented by the DStransmitter 610 and the collocated xTU-Os 311 and 411 or any other DSLoffice-side equipment such as the DPUs 310 and 410 when communicatingwith collocated remote NEs such as the xTU-Rs 321 and 421 and the DSreceivers 630 in a network such as the systems 300 and 400. At step 810,a plurality of encoded signals associated with a plurality of DSchannels in a network is obtained. The plurality of DS channels form aplurality of DS MIMO groups such as the MIMO groups 330, 450, 460, and640. The plurality of DS channels may be generated from differentialmode only or from any of the configurations 500 and 510. The pluralityof DS channels is represented by a channel matrix as shown in equation(3). At step 820, MIMO pre-coding is performed on the plurality ofencoded signals according to the plurality of MIMO groups, for example,by employing MIMO pre-coders such as the MIMO pre-coders 611. Forexample, a first subset of the plurality of DS channels form a first DSMIMO group of the plurality of DS MIMO groups and MIMO pre-coding isperformed by multiplying a second subset of the plurality of encodedsignals associated with the first subset of the plurality DS channels bya MIMO pre-coding matrix computed according to equation (5). At step830, crosstalk pre-coding is performed on the plurality of encodedsignals jointly after performing the MIMO pre-coding to produce aplurality of output signals, for example, by employing a DS FEXTpre-coder such as the DS FEXT pre-coder 612. The crosstalk pre-coding isperformed by multiplying the plurality of encoded signals by a FEXTpre-coding matrix computed according to equation (9) or (14). At step840, the plurality of output signals is substantially synchronouslytransmitted to a plurality of remote NEs via the plurality of DSchannels. The method 800 may be repeated for each subcarrier in thesystem.

FIG. 9 is a flowchart of an embodiment of a method 900 of performing USMU-MIMO DSL processing. The method 900 is implemented by the US receiver710 and the collocated xTU-Os 311 and 411 or any other DSL office-sideequipment such as the DPUs 310 and 410 when communicating withcollocated or non-collocated remote NEs such as the xTU-Rs 321 and 421and the US receivers 710 in a network such as the systems 300 and 400.At step 910, a plurality of modulated signals is received from theplurality of remote NEs via a plurality of US channels, where theplurality of US channels form a plurality of US MIMO groups such as theMIMO groups 330, 450, 460, and 740. The plurality of modulated signalsis MIMO pre-coded, for example, generated by using the MIMO pre-coders732 and the method 1400, as described more fully below. The plurality ofUS channels may be generated from differential mode only or from any ofthe configurations 500 and 510. The plurality of US channels isrepresented by a channel matrix as shown in equation (3). The firstmodulated signal is received from the first US channel and the secondmodulated signal is received from the second US channel. At step 915,FFT is performed on the plurality of the modulated signals to produce aplurality of demodulated signals. At step 920, frequency-domainequalization is performed on the plurality of demodulated signals, forexample, by employing FEQs such as the FEQs 714, to produce a pluralityof equalized demodulated signals. At step 930, crosstalk cancellation isperformed on the plurality of equalized demodulated signals jointly, forexample, by using a US FEXT canceller such as the US FEXT canceller 713.The crosstalk cancellation is performed by multiplying the plurality ofequalized demodulated signals by a FEXT cancellation matrix computedaccording to equation (16) or (18). At step 940, MIMO post-coding isperformed on the plurality of equalized demodulated signals according tothe plurality of US MIMO groups after performing the crosstalkcancellation, for example, by using MIMO post-coders such as the MIMOpost-coders 712. For example, a first subset of the plurality of USchannels form a first US MIMO group of the plurality of US MIMO groupsand the MIMO post-coding is performed by multiplying a second subset ofthe plurality of equalized demodulated signals associated with the firstsubset of the plurality of US channels by a MIMO post-coding matrixcomputed according to equations (4) to (7). The method 900 may berepeated for each subcarrier in the system

FIG. 10 is a flowchart of an embodiment of a method 1000 of determiningMIMO matrix coefficients for a MU-MIMO DSL system such as the systems300 and 400. The method 1000 is implemented by the DS transmitter 610,the US transmitter 730, or any other DSL office-side equipment such asthe DPUs 310 and 410 when communicating with collocated remote NEs suchas the xTU-Rs 321 and 421 and the DS receivers 630 and US receivers in anetwork such as the systems 300 and 400. The method 1000 is suitable foruse in both the US and DS directions. The method 1000 is implementedwhen determining a MIMO pre-coding matrix for the MIMO pre-coder 611 and732 and a MIMO post-coding matrix for MIMO post-coders 633 and 712. Themethod 1000 begins after estimating channels such as channels generatedby the cable bundles 620 and 720, for example, according to the channelmatrix shown in equation (3). For example, a first subset of thechannels forms a first MIMO group. At step 1010, a MIMO channelsub-matrix, denoted as H_(i,i), for a first subcarrier is obtained,where i is a positive integer identifying the MIMO group in the channelmatrix. The MIMO channel sub-matrix H_(i,i) comprises diagonal entriesrepresenting first direct channel estimates of the first subset ofchannels at the first subcarrier and off-diagonal entries representingfirst FEXT channel estimates of the first subset of the channels at thefirst subcarrier. At step 1020, the MIMO channel sub-matrix H_(i,i) isdecomposed into a first matrix, denoted as A_(i,i), a second matrix,denoted as W_(i,i), and a third matrix, denoted as B_(i,i), according toequation (20). The matrix decomposition may also be performed by usingSVD as shown in equation (5) or GMD as shown in equation (19). Themethod 1000 may be repeated for each subcarrier in the system.

FIG. 11 is a flowchart of an embodiment of a method 1100 of determiningFEXT mitigation matrix coefficients for a MU-MIMO DSL system such as thesystems 300 and 400. The method 1100 is implemented by collocated xTU-Ossuch as the xTU-Os 311 and 411, the DS transmitter 610, the US receiver710, or any other DSL office-side equipment such as the DPUs 310 and 410when communicating with collocated xTU-Rs such as the xTU-Rs 321 and421, the DS receivers 630, and the US transmitters 730 in a system suchas the systems 300 and 400. The method 1100 is suitable for use in boththe US and DS directions. The method 1100 is implemented whendetermining a DS FEXT pre-coding matrix for a DS FEXT pre-coder 611 or aUS FEXT cancellation matrix for a US FEXT canceller 713. The method 1100begins after obtaining direct channel estimates and FEXT channelestimates of a plurality of channels such as channels generated by thecable bundles 620 and 720. At step 1110, a first channel matrix, denotedas H, comprising diagonal entries representing the direct channelestimates and first off-diagonal entries representing FEXT channelestimates of the plurality of channels at a first subcarrier isobtained. The first channel matrix His as shown in equation (3). A firstdiagonal block, denoted as H_(i,i), of the first channel matrix Hrepresents MIMO channels in a MIMO group such as the MIMO groups MIMOgroups 330, 450, 460, 640, and 740 within the plurality of channels,where i is a positive integer identifying the MIMO group in the channelmatrix. At step 1120, a MIMO channel matrix H_(M) comprising the firstdiagonal blocks of the first channel matrix and off-diagonal blockscomprising values of zeros is generated, for example, according toequation (6). At step 1130, the first channel matrix is inverted toproduce a first inverted channel matrix H⁻¹. At step 1140, the MIMOchannel matrix and the first inverted channel matrix are multiplied toproduce a FEXT mitigation matrix. In the DS direction, themultiplication is performed according to equation (9) and the FEXTmitigation matrix is used as a DS FEXT pre-coding matrix. In the USdirection, the multiplication is performed according to equation (16)and the FEXT mitigation matrix is used as a US FEXT cancellation matrix.In an alternative embodiment, the steps 1130 and 1140 are combined. Inthe DS direction, the FEXT pre-coding matrix is computed according to aninverse of the first channel matrix H multiplied by the MIMO channelmatrix H_(M), for example, where the multiplication is computed withoutcomputation of inversion of H, for example, by employing matrixdecomposition. In the US direction, the FEXT cancellation matrix iscomputed according to the MIMO channel matrix H_(M) multiplied by aninverse of the first channel matrix H, for example, where themultiplication is computed without computation of inversion of H, forexample, by employing matrix decomposition.

FIG. 12 is a flowchart of another embodiment of a method 1200 ofdetermining FEXT mitigation matrix coefficients for a MU-MIMO DSL systemsuch as the systems 300 and 400. The method 1200 is implemented bycollocated xTU-Os such as the xTU-Os 311 and 411, the DS transmitter610, the US receiver 710, or any other DSL office-side equipment such asthe DPUs 310 and 410 when communicating with collocated xTU-Rs such asthe xTU-Rs 321 and 421, the DS receivers 630, and the US transmitters730 in a system such as the systems 300 and 400. The method 1200 issuitable for use in both the US and DS directions. The method 1200 is analternative of the method 1100. The method 1200 is implemented whendetermining a DS FEXT pre-coding matrix for a DS FEXT pre-coder 612 or aUS FEXT cancellation matrix for a US FEXT canceller 713. The method 1200begins after determining MIMO pre-coding matrices and MIMO post codingmatrices by employing the method 1000 and while performing MIMOpre-coding and MIMO post-coding, but before performing FEXT pre-codingor FEXT cancellation. At step 1210, second direct channel estimates of aplurality of channels at a first subcarrier, second FEXT channelestimates within each of the plurality of MIMO groups at the firstsubcarrier, and third FEXT channel estimates across the plurality ofMIMO groups at the first subcarrier are obtained after performing MIMOprocessing and prior to performing crosstalk processing. For example,the second direct channel estimates and the second FEXT channelestimates are computed while a transmitter performs MIMO pre-coding anda corresponding receiver performs MIMO post-coding. Thus, the seconddirect channel estimates and the second FEXT channel estimates are MIMOpre-coded and MIMO post-coded channel estimates. At step 1220, a secondchannel matrix comprising second diagonal entries representing thesecond direct channel estimates, second diagonal blocks each comprisingsecond off-diagonal entries representing corresponding second FEXTchannel estimates within each MIMO group, and second off-diagonal blocksrepresenting the third FEXT estimates across the MIMO groups aregenerated as shown in equation (13). At step 1230, second off-diagonalentries of each second diagonal block are assigned values of zeros. Forexample, the second off-diagonal entries within a MIMO group correspondto m′_(ij), n′_(ij), and l′_(ij) in equation (13). At step 1240, thesecond DS channel matrix is inverted to produce a FEXT mitigationmatrix. In the DS direction, the FEXT mitigation matrix is used as a DSFEXT pre-coding matrix. In the US direction, the FEXT mitigation matrixis used as a US FEXT cancellation matrix.

FIG. 13 is a flowchart of another embodiment of a method 1300 ofperforming DS MU-MIMO DSL processing. The method 1300 is implemented bya DSL remote-side apparatus such as the xTU-Rs 321 and 421 collocated ata single residence such as the residences 320, 430, or 440 and the DSreceivers 630 when communicating with a DSL office-side equipment suchas the collocated xTU-Os 311 and 411, the DPUs 310 and 410 in a systemsuch as the systems 300 and 400. The method 1300 employs similarmechanisms as the DS receivers 630. The collocated xTU-Rs andcorresponding collocated xTU-Os form a DS MIMO group such as the MIMOgroups 330, 450, 460, and 640. The method 1300 begins after obtaining aMIMO post-coding matrix such as S_(i,i) ⁻¹×U_(i,i) ^(H) computed fromequation (5), G_(i,i) ⁻¹×Q_(i,i) ^(H) computed from equation (19), orW_(i,i) ⁻¹×A_(i,i) ⁻¹ computed from equation (20) for the DS MIMO group.At step 1310, a plurality of DS signals is received from the DSLoffice-side apparatus via a subset of a plurality of DS channels formingthe DS MIMO group. The plurality of DS signals are pre-coded accordingto a DS MIMO pre-coding matrix such as V_(i,i) in equation (5), T_(i,i)in equation (19), and B_(i,i) in equation (5) associated with the DSMIMO group at a first subcarrier and according to a DS FEXT pre-codingmatrix associated with DS FEXT channels of the plurality of DS channelsat the first subcarrier. At step 1320, MIMO post-coding is performed onthe plurality of DS signals according to the DS MIMO post-coding matrixassociated with the DS MIMO group. The MIMO post-coding is performedafter performing frequency domain equalization at the receiver.

FIG. 14 is a flowchart of another embodiment of a method 1400 ofperforming US MU-MIMO DSL processing. The method 1400 is implemented bya DSL remote-side apparatus such as the xTU-Rs 321 and 421 collocated ata single residence such as the residences 320, 430, or 440 and the USreceivers 710 when communicating with a DSL office-side equipment suchas the collocated xTU-Os 311 and 411, the DPUs 310 and 410 in a systemsuch as the systems 300 and 400. The method 1400 employs similarmechanisms as the US transmitters 730. The collocated xTU-Rs andcorresponding collocated xTU-Os form a US MIMO group such as the MIMOgroups 330, 450, 460, and 740. The method 1400 begins after obtaining aMIMO pre-coding matrix such as V_(i,i) in equation (5), T_(i,i) inequation (19), or B_(i,i) in equation (20) for the US MIMO group. Atstep 1410, a plurality of encoded signals associated with a plurality ofUS channels forming the US MIMO group is obtained. At step 1420, theplurality of encoded signals is multiplied by US MIMO pre-codingmatrices such as such as V_(i,i) computed from equation (5), T_(i,i)computed from equation (19), or B_(i,i) computed from equation (20) toproduce a plurality of output signals.

FIG. 15 is a schematic diagram of an embodiment of a NE 1500. The NE1500 may be a DPU such as the DPUs 110, 210, 310, 410, collocated xTU-Ossuch as the xTU-Os 111, 211, 311, 411, a DS transmitter such as the DStransmitter 610, and a US receiver such as the US receiver 710. The NE1500 may also be DS receivers such as the DS receivers 630, and UStransmitters such as the US transmitters 730 in a DSL system such as theDSL systems 300 and 400. NE 1500 may be configured to implement and/orsupport the FEXT utilization and mitigation mechanisms and schemesdescribed herein. NE 1500 may be implemented in a single node or thefunctionality of NE 1500 may be implemented in a plurality of nodes. Oneskilled in the art will recognize that the term NE encompasses a broadrange of devices of which NE 1500 is merely an example. NE 1500 isincluded for purposes of clarity of discussion, but is in no way meantto limit the application of the present disclosure to a particular NEembodiment or class of NE embodiments.

At least some of the features/methods described in the disclosure areimplemented in a network apparatus or component, such as an NE 1500. Forinstance, the features/methods in the disclosure may be implementedusing hardware, firmware, and/or software installed to run on hardware.The NE 1500 is any device that transports packets through a network,e.g., a DSL access module (DSLAM), a DSL router, bridge, server, aclient, etc. As shown in FIG. 15, the NE 1500 comprises transceivers(Tx/Rx) 1510, which may be transmitters, receivers, or combinationsthereof. The Tx/Rx 1510 is coupled to a plurality of ports 1520 fortransmitting and/or receiving frames from other nodes. For example, theNE 1500 operates as a DSLAM at a DPU, communicates signal through a setof ports 1520 with remote DSL CPEs, and communicates signal through theother set of ports 1520 with a backbone network. In another example, theNE 1500 operates as a DSL CPE router, communicates signal through a setof ports 1520 with the DSLAM at DPU, and communicates through anotherset of ports with local devices inside a residence such as a laptopcomputer.

A processor 1530 is coupled to each Tx/Rx 1510 to process the framesand/or determine which nodes to send the frames to. The processor 1530may comprise one or more multi-core processors and/or memory devices1532, which may function as data stores, buffers, etc. The processor1530 may be implemented as a general purpose processor or may be part ofone or more application specific integrated circuits (ASICs) and/ordigital signal processors (DSPs). The processor 1530 may comprise a FEXTutilization and mitigation module 1533.

The FEXT utilization and mitigation module 1533 implements MIMOpre-coding, MIMO post-coding, FEXT pre-coding, and FEXT cancellationdepending on the embodiments as described in the methods 800, 900, 1000,and 1100, 1200, 1300, and 1400, and/or any other flowcharts, schemes,and methods discussed herein. As such, the inclusion of the FEXTutilization and mitigation 1533 and associated methods and systemsprovide improvements to the functionality of the NE 1500. Further, theFEXT utilization and mitigation 1533 effects a transformation of aparticular article (e.g., the DSL system) to a different state. In analternative embodiment, the FEXT utilization and mitigation 1533 may beimplemented as instructions stored in the memory device 1532, which maybe executed by the processor 1530.

The memory 1532 comprises one or more disks, tape drives, andsolid-state drives and may be used as an over-flow data storage device,to store programs when such programs are selected for execution, and tostore instructions and data that are read during program execution. Thememory 1532 may be volatile and non-volatile and may be read-only memory(ROM), random-access memory (RAM), ternary content-addressable memory(TCAM), and static random-access memory (SRAM).

Although the disclosed embodiments are described in the context of a DSLsystem where FEXT is the interference to be utilized within each MIMOgroup and cancelled across MIMO groups, the disclosed embodiments aresuitable for use in any MU-MIMO communication system such as a wirelesssystem and an IEEE 802.11 wireless local area network (WiFi) system. Forexample, a WiFi system employing MU-MIMO while communicating withmultiple MIMO devices may benefit from the disclosed MU-MIMO processingmechanisms. In wireless systems, FEXT is referred to co-channelinterference and is a signal received at a receiver from an un-intendedtransmitter antenna. In wireless systems, DS is referred to as downlink(DL) and US is referred to as uplink (UL).

While several embodiments have been provided in the present disclosure,it should be understood that the disclosed systems and methods might beembodied in many other specific forms without departing from the spiritor scope of the present disclosure. The present examples are to beconsidered as illustrative and not restrictive, and the intention is notto be limited to the details given herein. For example, the variouselements or components may be combined or integrated in another systemor certain features may be omitted, or not implemented.

In an embodiment, a NE includes means for obtaining a plurality ofencoded signals associated with a plurality of DS channels in a network,wherein the plurality of DS channels form a plurality of DS MIMO groups,means for performing, via the processor, MIMO pre-coding on theplurality of encoded signals according to the plurality of DS MIMOgroups, means for performing, via the processor, crosstalk pre-coding onthe plurality of encoded signals jointly after performing the MIMOpre-coding to produce a plurality of output signals, and means forsubstantially synchronously transmitting, via transmitters of the NE,the plurality of output signals to a plurality of remote NEs via theplurality of DS channels.

In an embodiment, a communication system office-side apparatus includesmeans for obtaining a plurality of encoded signals associated with aplurality of DS channels in a network, wherein the plurality of DSchannels form a plurality of DS MIMO groups, means for performing MIMOpre-coding on the plurality of encoded signals according to theplurality of DS MIMO groups, means for performing crosstalk pre-codingon the plurality of encoded signals jointly after performing the MIMOpre-coding to produce a plurality of output signals, and means forsubstantially synchronously transmitting the plurality of output signalsto a plurality of remote NEs via the plurality of DS channels.

In an embodiment, a DSL remote-side apparatus includes means forreceiving a plurality of downstream (DS) signals from a DSL office-sideapparatus via a subset of a plurality of DS channels forming a DSmultiple-input multiple-output (MIMO) group, wherein the plurality of DSsignals are pre-coded according to a DS MIMO pre-coding matrixassociated with the DS MIMO group at a first subcarrier and according toa DS far-end crosstalk (FEXT) pre-coding matrix associated with DS FEXTchannels of the plurality of DS channels at the first subcarrier, andmeans for performing MIMO post-coding on the plurality of DS signalsaccording to a DS MIMO post-coding matrix associated with the DS MIMOgroup.

In addition, techniques, systems, subsystems, and methods described andillustrated in the various embodiments as discrete or separate may becombined or integrated with other systems, modules, techniques, ormethods without departing from the scope of the present disclosure.Other items shown or discussed as coupled or directly coupled orcommunicating with each other may be indirectly coupled or communicatingthrough some interface, device, or intermediate component whetherelectrically, mechanically, or otherwise. Other examples of changes,substitutions, and alterations are ascertainable by one skilled in theart and could be made without departing from the spirit and scopedisclosed herein.

What is claimed is:
 1. A method implemented in a wireless networkelement (NE), comprising: obtaining, via a processor of the wireless NE,a plurality of encoded signals associated with a plurality of downstream(DS) channels in a wireless communication network, wherein the pluralityof DS channels form a plurality of DS multiple-input and multiple-output(MIMO) groups; performing, via the processor, MIMO pre-coding on theplurality of encoded signals according to the plurality of DS MIMOgroups to produce MIMO pre-coder output signals of the plurality of DSMIMO groups; performing, via the processor, a crosstalk pre-codingacross the MIMO groups using a crosstalk pre-coding matrix on the MIMOpre-coder output signals of the plurality of DS MIMO groups to produce aplurality of output signals, with the crosstalk pre-coding matrixcomputed according to a first DS channel matrix and a DS MIMO channelmatrix; wherein the first DS channel matrix comprises first diagonalentries representing first direct channel estimates of the plurality ofDS channels at a first subcarrier and first off-diagonal entriesrepresenting co-channel interference estimates of the plurality of DSchannels at the first subcarrier, a first diagonal block of the first DSchannel matrix representing MIMO channels in a first DS MIMO group ofthe plurality of DS MIMO groups; and wherein the DS MIMO channel matrixcomprises a second diagonal block and off-diagonal blocks, the seconddiagonal block corresponding to the first diagonal block of the first DSchannel matrix, and with the off-diagonal blocks comprising values ofzeros; and synchronously transmitting, via one or more transmitters ofthe wireless NE, the plurality of output signals to a plurality ofremote wireless NEs via the plurality of DS channels.
 2. The method ofclaim 1, wherein a first subset of the plurality of DS channels forms afirst DS MIMO group of the plurality of DS MIMO groups, wherein themethod further comprises receiving, via receivers of the NE, a MIMOpre-coding matrix for the first DS MIMO group at a first subcarrier,wherein the MIMO pre-coding matrix is decomposed from a DS MIMO channelmatrix comprising direct channel estimates of the first subset of theplurality of DS channels at the first subcarrier and crosstalk channelestimates of the first subset of the plurality of DS channels at thefirst subcarrier.
 3. The method of claim 2, wherein performing the MIMOpre-coding comprises multiplying a subset of the plurality of encodedsignals associated with the first DS MIMO group by the MIMO pre-codingmatrix.
 4. The method of claim 1, further comprising computing, via theprocessor, the crosstalk pre-coding matrix according to a product of aninverse of the first DS channel matrix and the DS MIMO channel matrix.5. The method of claim 4, wherein the crosstalk pre-coding is performedacross the MIMO groups by multiplying the plurality of encoded signalsby the crosstalk pre-coding matrix.
 6. The method of claim 1, furthercomprising obtaining, via the processor, direct channel estimates of theplurality of DS channels at a first subcarrier, second crosstalk channelestimates within each of the plurality of DS MIMO groups at the firstsubcarrier, and third crosstalk channel estimates across the pluralityof DS MIMO groups at the first subcarrier after performing the MIMOpre-coding and prior to performing the crosstalk pre-coding.
 7. Themethod of claim 6, wherein the direct channel estimates and the secondcrosstalk channel estimates are MIMO pre-coded and MIMO post-codedchannel estimates.
 8. A wireless network element (NE), comprising: aplurality of multiple-input and multiple-output (MIMO) pre-codersconfigured to perform MIMO pre-coding on a plurality of encoded signalsassociated with a plurality of downstream (DS) channels in a wirelesscommunication network according to a plurality of DS MIMO groups toproduce MIMO pre-coder output signals of the plurality of DS MIMOgroups, wherein the plurality of DS channels form a plurality of DSmultiple-input and multiple-output (MIMO) groups; a crosstalk pre-coderconfigured to perform a crosstalk pre-coding across the MIMO groupsusing a crosstalk pre-coding matrix on the MIMO pre-coder output signalsof the plurality of DS MIMO groups to produce a plurality of outputsignals, with the crosstalk pre-coding matrix computed according to afirst DS channel matrix and a DS MIMO channel matrix; and one or moretransmitters configured to synchronously transmit the plurality ofoutput signals to a plurality of remote wireless NEs via the pluralityof DS channels; wherein the first DS channel matrix comprises firstdiagonal entries representing first direct channel estimates of theplurality of DS channels at a first subcarrier and first off-diagonalentries representing co-channel interference estimates of the pluralityof DS channels at the first subcarrier, a first diagonal block of thefirst DS channel matrix representing MIMO channels in a first DS MIMOgroup of the plurality of DS MIMO groups; and wherein the DS MIMOchannel matrix comprises a second diagonal block and off-diagonalblocks, the second diagonal block corresponding to the first diagonalblock of the first DS channel matrix, and with the off-diagonal blockscomprising values of zeros.
 9. The wireless NE of claim 8, wherein afirst subset of the plurality of DS channels forms a first DS MIMO groupof the plurality of DS MIMO groups, wherein the wireless NE furthercomprises a receiver configured to receive a MIMO pre-coding matrix forthe first DS MIMO group at a first subcarrier, wherein the MIMOpre-coding matrix is decomposed from a DS MIMO channel matrix comprisingdirect channel estimates of the first subset of the plurality of DSchannels at the first subcarrier and crosstalk channel estimates of thefirst subset of the plurality of DS channels at the first subcarrier.10. The wireless NE of claim 9, wherein the crosstalk pre-coder isfurther configured to multiply a subset of the plurality of encodedsignals associated with the first DS MIMO group by the MIMO pre-codingmatrix.
 11. The wireless NE of claim 8, wherein the crosstalk pre-codingmatrix is computed according to a product of an inverse of the first DSchannel matrix and the DS MIMO channel matrix.
 12. The wireless NE ofclaim 11, wherein the crosstalk pre-coding is performed across the MIMOgroups by multiplying the plurality of encoded signals by the crosstalkpre-coding matrix.
 13. The wireless NE of claim 8, further comprising aprocessor configured to obtain direct channel estimates of the pluralityof DS channels at a first subcarrier, second crosstalk channel estimateswithin each of the plurality of DS MIMO groups at the first subcarrier,and third crosstalk channel estimates across the plurality of DS MIMOgroups at the first subcarrier after performing the MIMO pre-coding andprior to performing the crosstalk pre-coding.
 14. The wireless NE ofclaim 13, wherein the direct channel estimates and the second crosstalkchannel estimates are MIMO pre-coded and MIMO post-coded channelestimates.
 15. A wireless network element (NE), comprising: a processorconfigured to: perform multiple-input and multiple-output (MIMO)pre-coding on a plurality of encoded signals associated with a pluralityof downstream (DS) channels in a wireless communication networkaccording to a plurality of DS MIMO groups to produce MIMO pre-coderoutput signals of the plurality of DS MIMO groups, wherein the pluralityof DS channels form a plurality of DS multiple-input and multiple-output(MIMO) groups; and crosstalk pre-coding across the MIMO groups using acrosstalk pre-coding matrix on the MIMO pre-coder output signals of theplurality of DS MIMO groups to produce a plurality of output signals,with the crosstalk pre-coding matrix computed according to a first DSchannel matrix and a DS MIMO channel matrix; and a transmitter coupledto the processor and configured to synchronously transmit the pluralityof output signals to a plurality of remote wireless NEs via theplurality of DS channels, wherein the first DS channel matrix comprisesfirst diagonal entries representing first direct channel estimates ofthe plurality of DS channels at a first subcarrier and firstoff-diagonal entries representing co-channel interference estimates ofthe plurality of DS channels at the first subcarrier, a first diagonalblock of the first DS channel matrix representing MIMO channels in afirst DS MIMO group of the plurality of DS MIMO groups; and wherein theDS MIMO channel matrix comprises a second diagonal block andoff-diagonal blocks, the second diagonal block corresponding to thefirst diagonal block of the first DS channel matrix, and with theoff-diagonal blocks comprising values of zeros.
 16. The wireless NE ofclaim 15, wherein a first subset of the plurality of DS channels forms afirst DS MIMO group of the plurality of DS MIMO groups, wherein theprocessor is further configured to receive a MIMO pre-coding matrix forthe first DS MIMO group at a first subcarrier.
 17. The wireless NE ofclaim 15, wherein the processor is further configured to compute thecrosstalk pre-coding matrix according to a product of an inverse of thefirst DS channel matrix and the DS MIMO channel matrix.
 18. The wirelessNE of claim 15, wherein the crosstalk pre-coding is performed across theMIMO groups by multiplying the plurality of encoded signals by thecrosstalk pre-coding matrix.
 19. The wireless NE of claim 15, whereinthe processor is further configured to obtain direct channel estimatesof the plurality of DS channels at a first subcarrier, second crosstalkchannel estimates within each of the plurality of DS MIMO groups at thefirst subcarrier, and third crosstalk channel estimates across theplurality of DS MIMO groups at the first subcarrier after performing theMIMO pre-coding and prior to performing the crosstalk pre-coding. 20.The wireless NE of claim 19, wherein the second direct channel estimatesand the second FEXT channel estimates are MIMO pre-coded and MIMOpost-coded channel estimates.